Verovatnoca I Statistika - Teorija
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Questions and Answers
- 1.
Verovatnoca je nauka koja izucava:
- A.
Slucajne pojave
- B.
Deterministicke pojave
- C.
Stohasticke pojave
- D.
Statisticke pojave
Correct Answer
A. Slucajne pojaveExplanation
The correct answer is "Slucajne pojave" which translates to "Random events" in English. This explanation suggests that probability is the science that studies random events, which are events that cannot be predicted with certainty. It implies that probability deals with situations where the outcome is uncertain and involves calculating the likelihood of different outcomes occurring.Rate this question:
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- 2.
Prvi problemi iz teorije verovatnoce su vezani za:
- A.
Kockarske probleme
- B.
Statisticke probleme
- C.
Trgovacke probleme
- D.
Naucne probleme
Correct Answer
A. Kockarske problemeExplanation
The first problems in the theory of probability were likely related to gambling. Gambling involves uncertain outcomes and the calculation of probabilities, making it a natural starting point for the development of probability theory.Rate this question:
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- 3.
Dogadjaj je slucajan ako:
- A.
Ne moze da se predvidi
- B.
Moze da se predvidi
- C.
Znamo njegove zakonomernosti
- D.
Ne znamo njegove zakonomernosti
Correct Answer
A. Ne moze da se predvidiExplanation
The correct answer is "Ne moze da se predvidi" which translates to "It cannot be predicted" in English. This answer suggests that a random event is one that cannot be foreseen or anticipated. It implies that there is no way to determine or predict the outcome or occurrence of the event beforehand.Rate this question:
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- 4.
Slucajan eksperiment mora da:
- A.
Moze da se ponavlja proizvoljan broj puta pri istim uslovima
- B.
Ne moze da se ponavlja proizvoljan broj puta pri istim uslovima
- C.
Svi njegovi ishodi nisu unapred definisani
- D.
Svi njegovi ishodi su unapred definisani
Correct Answer(s)
A. Moze da se ponavlja proizvoljan broj puta pri istim uslovima
D. Svi njegovi ishodi su unapred definisaniExplanation
A slucajan eksperiment is a random experiment. The answer states that it can be repeated an arbitrary number of times under the same conditions, indicating that the experiment can be replicated. Additionally, it states that all of its outcomes are predetermined, meaning that the possible results of the experiment are known in advance. Therefore, the answer suggests that a slucajan eksperiment is both repeatable and has predetermined outcomes.Rate this question:
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- 5.
Slucajan eksperiment mora da:
- A.
Ishod pojedinog eksperimenta je unapred poznat
- B.
Ishod pojedinog eksperimenta nije unapred poznat
- C.
Svi njegovi ishodi su unapred definisani
- D.
Moze da se ponavlja proizvoljan broj puta pri istim uslovima
Correct Answer(s)
B. Ishod pojedinog eksperimenta nije unapred poznat
C. Svi njegovi ishodi su unapred definisani
D. Moze da se ponavlja proizvoljan broj puta pri istim uslovimaExplanation
The correct answer is that the outcome of an individual experiment is not known in advance, all its outcomes are predetermined, and it can be repeated any number of times under the same conditions. This means that each time the experiment is conducted, the result cannot be predicted beforehand, but all possible outcomes are already defined. Additionally, the experiment can be repeated multiple times, and the conditions remain consistent throughout.Rate this question:
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- 6.
Klasicna definicija verovatnoce:
- A.
Definisao ju je Laplas
- B.
Odnosi se samo na konacne skupove
- C.
Nije bitan broj elemenata skupa
- D.
Svi ishodi imaju jednaku verovatnocu
Correct Answer(s)
A. Definisao ju je Laplas
B. Odnosi se samo na konacne skupove
D. Svi ishodi imaju jednaku verovatnocuExplanation
This answer states that the classical definition of probability was defined by Laplace, it applies only to finite sets, and all outcomes have equal probability.Rate this question:
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- 7.
Klasicna definicija verovatnoce odnosi se na eksperimente:
- A.
Ciji je skup dogadjaja konacan
- B.
Ciji je skup dogadjaja beskonacan
- C.
Ciji ishodi imaju jednake verovatnoce
- D.
Ciji ishodi imaju proizvoljne verovatnoce
Correct Answer(s)
A. Ciji je skup dogadjaja konacan
C. Ciji ishodi imaju jednake verovatnoceExplanation
The correct answer is "Ciji je skup dogadjaja konacan, Ciji ishodi imaju jednake verovatnoce." This is because the classical definition of probability applies to experiments with a finite set of events, where each event has an equal probability of occurring.Rate this question:
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- 8.
Ako je dogadjaj A da je sijalica proizvedena u prvoj fabrici, a dogadjaj B da je dobra, sta znaci dogadjaj ABc?
- A.
Sijalica je proizvedena u drugoj fabrici i dobra je
- B.
Sijalica je proizvedena u drugoj fabrici ili dobra je
- C.
Sijalica je proizvedena u prvoj fabrici i nije dobra
- D.
Sijalica je proizvedena u drugoj fabrici ili jedobra
Correct Answer
C. Sijalica je proizvedena u prvoj fabrici i nije dobraExplanation
The correct answer is "Sijalica je proizvedena u prvoj fabrici i nije dobra". This means that the event ABc represents the situation where the light bulb is produced in the first factory and is not good.Rate this question:
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- 9.
Ako je dogadjaj A da je sijalica proizvedena u prvoj fabrici, a dogadjaj B da je dobra, sta znaci dogadjaj A+B?
- A.
Sijalica je proizvedena u drugoj fabrici i dobra je
- B.
Sijalica je proizvedena u drugoj fabrici ili je dobra
- C.
Sijalica je proizvedena u prvoj fabrici i dobra je
- D.
Sijalica je proizvedena u prvoj fabrici ili je dobra
Correct Answer
D. Sijalica je proizvedena u prvoj fabrici ili je dobraExplanation
The event A represents the light bulb being produced in the first factory, and event B represents the light bulb being good. The event A+B means that either the light bulb was produced in the first factory or it is good.Rate this question:
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- 10.
Aksiomatiku verovatnoce definisao je:
- A.
Gaus
- B.
Ferma
- C.
Laplas
- D.
Kolmogorov
Correct Answer
D. KolmogorovExplanation
The correct answer is Kolmogorov. Kolmogorov is known for his work in probability theory, where he defined the axioms of probability. His work laid the foundations for modern probability theory and provided a rigorous mathematical framework for studying uncertainty and randomness.Rate this question:
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- 11.
Aksime teorije verovatnoce su:
- A.
Verovatnoca sigurnog dogadjaja jednaka je 1
- B.
Verovatnoca je broj veci od 1
- C.
Verovatnoca je broj manji od 0
- D.
Verovatnoca je broj u intervalu od 0 do 1
Correct Answer(s)
A. Verovatnoca sigurnog dogadjaja jednaka je 1
D. Verovatnoca je broj u intervalu od 0 do 1Explanation
The correct answer is "Verovatnoca sigurnog dogadjaja jednaka je 1" and "Verovatnoca je broj u intervalu od 0 do 1". This is because in probability theory, the probability of a certain event occurring is always 1, as it is guaranteed to happen. Additionally, probabilities are always expressed as numbers between 0 and 1, where 0 represents an impossible event and 1 represents a certain event.Rate this question:
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- 12.
Aksime teorije verovatnoce su:
- A.
Verovatnoca sigurnog dogadjaja je jednaka 0
- B.
Verovatnoca zbira dogadjaja jednaka je zbiru verovatnoca tih dogadjaja
- C.
Verovatnoca nemoguceg dogadjaja je jednaka 0
- D.
Verovatnoca je broj u intervalu od 0 do 1
Correct Answer(s)
B. Verovatnoca zbira dogadjaja jednaka je zbiru verovatnoca tih dogadjaja
D. Verovatnoca je broj u intervalu od 0 do 1Explanation
The correct answer states that the probability of the sum of events is equal to the sum of their individual probabilities. This is a fundamental principle in probability theory known as the addition rule. Additionally, the answer correctly states that probability is a number between 0 and 1, inclusive. This is because probabilities represent the likelihood of an event occurring, with 0 indicating impossibility and 1 indicating certainty.Rate this question:
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- 13.
Suprotan dogadjaj dogadjaju A:
- A.
Se realizuje kada se dogadjaj A ne realizuje
- B.
Se realizuje istovremeno kada i dogadjaj A
- C.
Iznosi 1-P(A)
- D.
Iznosi 1+P(A)
Correct Answer(s)
A. Se realizuje kada se dogadjaj A ne realizuje
C. Iznosi 1-P(A)Explanation
The correct answer is "Se realizuje kada se dogadjaj A ne realizuje" and "Iznosi 1-P(A)". This means that the complementary event of event A occurs when event A does not occur. The probability of the complementary event is equal to 1 minus the probability of event A.Rate this question:
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- 14.
Suprotan dogadjaj dogadjaju "Pojava 2 glave pri bacanju 2 dinara " je:
- A.
2 pisma
- B.
Bar 1 pismo
- C.
Bar 1 glava
- D.
1 pismo
Correct Answer
B. Bar 1 pismoExplanation
The explanation for the given correct answer "Bar 1 pismo" is that the event "Pojava 2 glave pri bacanju 2 dinara" refers to the occurrence of getting 2 heads when tossing 2 coins. The phrase "Bar 1 pismo" means "at least 1 tails" in Serbian. So, the answer "Bar 1 pismo" implies that there is at least 1 tails when tossing the 2 coins, which is the opposite of the given event.Rate this question:
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- 15.
Suprotan dogadjaj dogadjaju " Ne vise od 2 pogotka u 5 gadjanja " je
- A.
Manje od 2 pogotka
- B.
Vise od 2 pogotka
- C.
3 pogotka
- D.
3 promasaja
Correct Answer
B. Vise od 2 pogotkaExplanation
The correct answer is "Vise od 2 pogotka" (More than 2 hits). This means that the event "Ne vise od 2 pogotka u 5 gadjanja" (Not more than 2 hits in 5 shots) is referring to the outcome of getting more than 2 hits. Therefore, the correct answer is the one that represents this outcome.Rate this question:
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- 16.
Skup svih povoljnih realizacija dogadjaja " Vadjenje 2 crvene kuglice iz kese u kojoj se nalaze 5 crvenih i 4 zelene kuglice " je:
- A.
5
- B.
10
- C.
20
- D.
2
Correct Answer
B. 10Explanation
The question is asking for the number of favorable outcomes in the event of drawing 2 red balls from a bag containing 5 red balls and 4 green balls. To find the number of favorable outcomes, we need to calculate the number of ways to choose 2 red balls from the 5 available. This can be done using the combination formula, which is given by nCr = n! / (r!(n-r)!). In this case, n = 5 (number of red balls) and r = 2 (number of balls to be chosen). Plugging in the values, we get 5C2 = 5! / (2!(5-2)!) = 5! / (2!3!) = (5*4*3!) / (2!3!) = (5*4) / (2*1) = 10. Therefore, the answer is 10.Rate this question:
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- 17.
Skup svih ishoda nekog dogadjaja je:
- A.
Proizvoljan dogadjaj
- B.
Siguran dogadjaj
- C.
Nemoguc dogadjaj
- D.
Verovatnoca mu je 1
Correct Answer(s)
B. Siguran dogadjaj
D. Verovatnoca mu je 1Explanation
The correct answer is "Siguran dogadjaj, Verovatnoca mu je 1". A siguran dogadjaj refers to an event that is certain to occur. In this case, the skup svih ishoda (set of all outcomes) of some event is being described as a siguran dogadjaj with a probability of 1. This means that every outcome in the set is guaranteed to happen, and there is no possibility of any other outcome occurring.Rate this question:
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- 18.
Skup svih ishoda dogadjaja " Bacanje 3 novcica " ima:
- A.
2 elementa
- B.
6 elemenata
- C.
36 elemenata
- D.
8 elemenata
Correct Answer
D. 8 elemenataExplanation
The correct answer is 8 elements because when you toss 3 coins, each coin can have 2 possible outcomes (heads or tails). Since there are 3 coins, the total number of possible outcomes is 2 * 2 * 2 = 8.Rate this question:
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- 19.
Verovatnoca da prilikom bacanja 3 novcica dobijemo 3 puta glavu je:
- A.
0.5
- B.
0.125
- C.
0.225
- D.
0.25
Correct Answer
B. 0.125Explanation
The probability of getting three heads when flipping three coins is 0.125. This can be calculated by multiplying the probability of getting a head on one coin flip (0.5) by itself three times, since each coin flip is an independent event. Therefore, 0.5 * 0.5 * 0.5 = 0.125.Rate this question:
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- 20.
Verovatnoca je preslikavanje:
- A.
Realnih brojeva u skup slucajnih dogadjaja
- B.
Slucajnih dogadjaja su skup svih realnih brojeva
- C.
Slucajnih dogadjaja u interval (0,1)
- D.
Slucajnih dogadjaja u interval [0,1]
Correct Answer
D. Slucajnih dogadjaja u interval [0,1]Explanation
The correct answer is "Slucajnih dogadjaja u interval [0,1]". This is because probability is a mapping of random events to the interval [0,1]. The probability of an event can range from 0 (impossible event) to 1 (certain event). Therefore, the correct answer is the option that mentions random events in the interval [0,1].Rate this question:
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- 21.
Skup svih ishoda dogadjaja " Bacanje 2 kocke " ima:
- A.
2 elementa
- B.
6 elemenata
- C.
36 elemenata
- D.
8 elemenata
Correct Answer
C. 36 elemenataExplanation
The correct answer is 36 elements because when two dice are thrown, each dice has six possible outcomes (numbers 1 to 6). Therefore, the total number of outcomes when throwing two dice is 6 multiplied by 6, which equals 36.Rate this question:
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- 22.
Statisticka definicija verovatnoce je:
- A.
Rezultat prakse
- B.
Rezultat apstrakcije
- C.
Oslanja se na relativnu ucestalost
- D.
Ne oslanja se na relativnu ucestalost
Correct Answer(s)
A. Rezultat prakse
C. Oslanja se na relativnu ucestalostExplanation
The correct answer is "Rezultat prakse, Oslanja se na relativnu ucestalost." This is because the statistical definition of probability is based on empirical observations and practical experience. It involves studying the frequency or likelihood of an event occurring in relation to the total number of possible outcomes. Therefore, it is a result of practical observations and relies on the relative frequency of events.Rate this question:
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- 23.
Ovaj izraz predstavlja:
- A.
Statisticku definiciju verovatnoce
- B.
Laplasovu definiciju verovatnoce
- C.
Klasicnu definiciju verovatnoce
- D.
Apriori- definiciju verovatnoce
Correct Answer
A. Statisticku definiciju verovatnoceExplanation
This expression represents the statistical definition of probability.Rate this question:
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- 24.
Ako je zadovoljena veza
- A.
Dogadjaji A cine potpuni sistem
- B.
Dogadjaji A ne cine potpuni sistem
- C.
Unija dogadjaja A je skup svih elementarnih dogadjaja
- D.
Unija dogadjaja A je podskup svih elementarnih dogadjaja
Correct Answer(s)
A. Dogadjaji A cine potpuni sistem
C. Unija dogadjaja A je skup svih elementarnih dogadjajaExplanation
The correct answer is "Dogadjaji A cine potpuni sistem". This means that the events A form a complete system, indicating that there are no other events outside of A that need to be considered. Additionally, the answer states that "Unija dogadjaja A je skup svih elementarnih dogadjaja", meaning that the union of events A is the set of all elementary events. This implies that all possible outcomes are included in the events A.Rate this question:
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- 25.
Nemoguc dogadjaj:
- A.
Ima verovatnocu 0
- B.
Ima verovatnocu 1
- C.
Je suprotan sigurnom dogadjaju
- D.
Je suprotan bilo kom dogadjaju
Correct Answer
A. Ima verovatnocu 0Explanation
This answer suggests that a "nemoguc dogadjaj" (impossible event) has a probability of 0. This means that the event cannot occur under any circumstances, making it completely unlikely or impossible to happen.Rate this question:
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- 26.
Siguran dogadjaj:
- A.
Ima verovatnocu 0
- B.
Ima verovatnocu 1
- C.
Je suprotan nemogucem dogadjaju
- D.
Je suprotan bilo kom dogadjaju
Correct Answer
B. Ima verovatnocu 1Explanation
The correct answer is "Ima verovatnocu 1" which means "It has a probability of 1". This implies that the event is certain to happen, meaning it is guaranteed to occur.Rate this question:
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- 27.
Ovaj izraz predstavlja:
- A.
Statisticku definiciju verovatnoce
- B.
Laplasovu definiciju verovatnoce
- C.
Klasicnu definiciju verovatnoce
- D.
Apriori- definiciju verovatnoce
Correct Answer(s)
B. Laplasovu definiciju verovatnoce
C. Klasicnu definiciju verovatnoce
D. Apriori- definiciju verovatnoceExplanation
The correct answer is Laplasovu definiciju verovatnoce, Klasicnu definiciju verovatnoce, Apriori- definiciju verovatnoce. This means that the given expression represents Laplace's definition of probability, the classical definition of probability, and the apriori definition of probability.Rate this question:
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- 28.
Oznaka Ω koristi se za oznacavanje:
- A.
Bilo kog dogadjaja
- B.
Skupa (prostora) elementarnih dogadjaja
- C.
Ne koristi se u verovatnoci
- D.
Nemoguceg dogadjaja
Correct Answer
B. Skupa (prostora) elementarnih dogadjajaExplanation
The symbol Ω is used to denote the sample space, which is the set of all possible outcomes or elementary events in a probability experiment. It represents the entire set of outcomes that could occur in a given situation. Therefore, the correct answer is "Skupa (prostora) elementarnih dogadjaja" which translates to "Set (space) of elementary events."Rate this question:
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- 29.
Ako se dogadjaji A i B medjusobno iskljucuju onda je verovatnocaa zbira dogadjaja:
- A.
P(A+B) = P(A) - P(B)
- B.
P(A+B) = P(A) + P(B)
- C.
P(A+B) = P(A) + P(B) + P(AB)
- D.
P(A+B) = P(A) + P(B) - P(AB)
Correct Answer
B. P(A+B) = P(A) + P(B)Explanation
The correct answer is P(A+B) = P(A) + P(B). This is because when events A and B are mutually exclusive, it means that they cannot occur at the same time. Therefore, the probability of the union of events A and B is equal to the sum of their individual probabilities.Rate this question:
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- 30.
Ako se dogadjaji A i B medjusobno ne iskljucuju onda je verovatnoca zbira dogadjaja:
- A.
P(A+B) = P(A) - P(B)
- B.
P(A+B) = P(A) + P(B)
- C.
P(A+B) = P(A) + P(B) + P(AB)
- D.
P(A+B) = P(A) + P(B) - P(AB)
Correct Answer
D. P(A+B) = P(A) + P(B) - P(AB)Explanation
The correct answer is P(A+B) = P(A) + P(B) - P(AB). This is known as the inclusion-exclusion principle in probability theory. It states that when events A and B are not mutually exclusive, the probability of their union is equal to the sum of their individual probabilities minus the probability of their intersection. This is because when we add the probabilities of A and B, we are counting the intersection (P(AB)) twice, so we need to subtract it once to correct for the overlap.Rate this question:
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- 31.
Ako se dogadjaji A, B i C medjusobno ne iskljucuju onda je verovatnoca zbira dogadjaja:
- A.
P(A+B+C) = P(A) + P(B) + P(C) + P(ABC)
- B.
P(A+B) = P(A) + P(B) + P(C)
- C.
P(A+B+C) = P(A) + P(B) + P(C) - P(AB) - P(AC) - P(BC) + P(ABC)
- D.
P(A+B) = P(A) + P(B) - P(AB) - P(AC) - P(BC)
Correct Answer
C. P(A+B+C) = P(A) + P(B) + P(C) - P(AB) - P(AC) - P(BC) + P(ABC)Explanation
The given answer is the formula for calculating the probability of the union of three events (A, B, and C) that do not mutually exclude each other. It states that the probability of the union of A, B, and C is equal to the sum of the individual probabilities of A, B, and C, minus the probabilities of the intersections between them (AB, AC, BC), and finally adding back the probability of the intersection of all three events (ABC). This formula accounts for the overlapping probabilities between the events, ensuring that they are not double-counted.Rate this question:
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- 32.
Dogadjaji A i B su nezavisni ako su:
- A.
Disjunktni
- B.
Realizacija jednog ne utice na realizaciju drugog
- C.
Realizacija jednog utice na realizaciju drugog
- D.
P(AB) = P(A) * P(B)
Correct Answer(s)
A. Disjunktni
B. Realizacija jednog ne utice na realizaciju drugog
D. P(AB) = P(A) * P(B)Explanation
The correct answer is "Disjunktni, Realizacija jednog ne utice na realizaciju drugog, P(AB) = P(A) * P(B)". This answer suggests that events A and B are independent. This means that the occurrence of one event does not affect the occurrence of the other event. Additionally, the probability of both events A and B happening together (P(AB)) is equal to the product of the individual probabilities of each event (P(A) * P(B)).Rate this question:
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- 33.
Dogadjaji A i B su nezavnisni ako je:
- A.
P(A/B) = P(A)
- B.
P(B/A) = P(B)
- C.
P(A/B) > P(A)
- D.
P(A/B) < P(A)
Correct Answer(s)
A. P(A/B) = P(A)
B. P(B/A) = P(B)Explanation
The given answer states that events A and B are independent if the conditional probability of A given B is equal to the probability of A, and the conditional probability of B given A is equal to the probability of B. This means that the occurrence of event B does not affect the probability of event A, and vice versa. In other words, the probabilities of events A and B are not dependent on each other.Rate this question:
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- 34.
U uslovnoj verovatnoci P(A/B):
- A.
Dogadjaj A se realizuje pod uslovom B
- B.
Dogadjaj B se realizuje pod uslovom A
- C.
Nije bitno koji se od dogadjaja A ili B uslov
- D.
P(A/B) = P(AB) / P(B)
Correct Answer
A. Dogadjaj A se realizuje pod uslovom BExplanation
This answer states that event A occurs under the condition of event B.Rate this question:
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- 35.
Uslovna verovatnoca P(A/B)
- A.
P(A/B) = P(AB) / P(B)
- B.
P(A/B) = P(AB) * P(B) / P(AB)
- C.
P(A/B) = P(AB) / P(A)
- D.
P(A/B) = P(AB) * P(B)
Correct Answer
A. P(A/B) = P(AB) / P(B)Explanation
The correct answer is P(A/B) = P(AB) / P(B). This is the formula for conditional probability, which calculates the probability of event A given that event B has occurred. It is obtained by dividing the probability of both events A and B occurring (P(AB)) by the probability of event B occurring (P(B)).Rate this question:
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- 36.
Verovatnoca proizvoda nezavisnih dogadjaja A i B je:
- A.
P(AB) = P(A/B) * P(B)
- B.
P(AB) = P(A) * P(B)
- C.
P(AB) = P(B/A) * P(B)
- D.
P(AB) = P(A) + P(B)
Correct Answer
B. P(AB) = P(A) * P(B)Explanation
The correct answer is P(AB) = P(A) * P(B). This is because the probability of the independent events A and B occurring together is equal to the probability of event A occurring multiplied by the probability of event B occurring. This formula is derived from the definition of independence, where the occurrence of one event does not affect the probability of the other event happening. Therefore, the probability of the product of two independent events is the product of their individual probabilities.Rate this question:
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- 37.
Verovatnoca proizvoda zavisnih dogadjaja A i B je:
- A.
P(AB) = P(A/B) * P(B)
- B.
P(AB) = P(A) * P(B)
- C.
P(AB) = P(B/A) * P(B)
- D.
P(AB) = P(A) + P(B)
Correct Answer
A. P(AB) = P(A/B) * P(B)Explanation
The correct answer is P(AB) = P(A/B) * P(B). This answer is derived from the definition of conditional probability. The probability of the joint occurrence of events A and B is equal to the probability of event A given event B, multiplied by the probability of event B. This formula is commonly used in probability calculations when dealing with dependent events.Rate this question:
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- 38.
Verovatnoca proizvoda zavisnih dogadjaja A, B i C je:
- A.
P(ABC) = P(AB/C) * P(B)
- B.
P(ABC) = P(A) * P(B) * P(C)
- C.
P(ABC) = P(B/A) * P(B/C)
- D.
P(ABC) = P(A) * P(B/A) * P(C/AB)
Correct Answer
D. P(ABC) = P(A) * P(B/A) * P(C/AB)Explanation
The given answer, P(ABC) = P(A) * P(B/A) * P(C/AB), is the correct explanation for the probability of the product of dependent events A, B, and C. This formula follows the principle of conditional probability, where the probability of event A occurring is multiplied by the probability of event B occurring given that event A has occurred (P(B/A)), and then further multiplied by the probability of event C occurring given that both events A and B have occurred (P(C/AB)). This formula accounts for the dependence between the events and calculates the probability of all three events occurring together.Rate this question:
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- 39.
Potpuni sistem hipoteza cine dogadjaji:
- A.
Cije su verovatnoce unapred poznate
- B.
Cije verovatnoce nisu unapred poznate
- C.
Ciji je zbir verovatnoca jednak 1
- D.
Ciji je zbir verovatnoca proizvoljan broj u [0,1]
Correct Answer(s)
A. Cije su verovatnoce unapred poznate
C. Ciji je zbir verovatnoca jednak 1Explanation
The correct answer is "Cije su verovatnoce unapred poznate, Ciji je zbir verovatnoca jednak 1." This answer suggests that the events in a complete system of hypotheses have known probabilities and the sum of these probabilities is equal to 1. This implies that all possible outcomes are accounted for and there is no uncertainty or ambiguity in the probabilities assigned to each hypothesis.Rate this question:
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- 40.
Bajesova formula zove se i:
- A.
Formula verovatnoca hipoteza
- B.
Formula verovatnoca uzorka
- C.
Formula totalne verovatnoce
- D.
Formula uslovne verovatnoce
Correct Answer(s)
A. Formula verovatnoca hipoteza
B. Formula verovatnoca uzorkaExplanation
The Bajesova formula is also known as the formula for probability of hypothesis and the formula for probability of sample.Rate this question:
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- 41.
Bacamo kocku i novcic. Dogadjaji da padne pismo i da padne broj 5 su:
- A.
Disjunktni
- B.
Nisu disjunktni
- C.
Nezavisni
- D.
Zavisni
Correct Answer
A. DisjunktniExplanation
The events "padne pismo" (coin lands on heads) and "padne broj 5" (dice lands on the number 5) are disjunct events because they cannot occur at the same time. If the coin lands on heads, it means the dice did not land on the number 5, and vice versa. Therefore, the correct answer is "Disjunktni."Rate this question:
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- 42.
Bacamo kocku. Dogadjaji da padne paran broj ili da padne broj 4 su:
- A.
Disjunktni
- B.
Nisu disjunktni
- C.
Nezavisni
- D.
Zavisni
Correct Answer
C. NezavisniExplanation
The events of rolling an even number and rolling a 4 are independent because the outcome of rolling an even number does not affect the outcome of rolling a 4, and vice versa. The probability of rolling an even number is 1/2, and the probability of rolling a 4 is 1/6. These probabilities do not change regardless of the outcome of the other event. Therefore, the events are independent.Rate this question:
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- 43.
Dogadjaji A, B i C su nezavisni i verovatnoce im iznose 1/2, 1/3 i 1/3. Koliko iznosi verovatnoca dogadjaja ABC?
- A.
1/9
- B.
1/18
- C.
1
- D.
2/3
Correct Answer
B. 1/18Explanation
The probability of event A, B, and C occurring independently can be calculated by multiplying their individual probabilities. Thus, the probability of event ABC occurring is (1/2) * (1/3) * (1/3) = 1/18.Rate this question:
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- 44.
Ako se dogadjaji A i B iskljucuju (disjunktni su) i P(A) = 0.3, P(B) = 0.5 onda je P(A+B)?
- A.
0.15
- B.
0.8
- C.
0.5
- D.
1
Correct Answer
B. 0.8Explanation
If events A and B are mutually exclusive (disjoint) and the probability of event A is 0.3 and the probability of event B is 0.5, then the probability of either event A or event B occurring (P(A+B)) is equal to the sum of their individual probabilities. Therefore, P(A+B) = P(A) + P(B) = 0.3 + 0.5 = 0.8.Rate this question:
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- 45.
Ako se dogadjaji A i B iskljucuju (disjunktni su) i P(A) = 0.3, P(B) = 0.5 onda je P(AB)?
- A.
0.2
- B.
0.15
- C.
0.85
- D.
0
Correct Answer
D. 0Explanation
If events A and B are mutually exclusive (disjoint) and P(A) = 0.3, P(B) = 0.5, then the probability of both events occurring (P(AB)) would be 0. Since mutually exclusive events cannot occur at the same time, the probability of both events happening simultaneously is zero.Rate this question:
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- 46.
Ako su P(A) i P(B) verovatnoce dva nezavisna dogadjaja A i B, onda je verovatnoca da ce se realizovati oba dogadjaja:
- A.
P(A) * P(B)
- B.
(1-P(A)) * (1-P(B))
- C.
P(A) * (1-P(B))
- D.
(1-P(A)) * P(B)
Correct Answer
A. P(A) * P(B)Explanation
The given correct answer, P(A) * P(B), is the formula for calculating the probability of two independent events A and B both occurring. This formula is derived from the multiplication rule of probability, which states that the probability of two independent events occurring together is equal to the product of their individual probabilities. Therefore, if P(A) and P(B) are the probabilities of events A and B occurring independently, then the probability of both events occurring is the product of these probabilities, P(A) * P(B).Rate this question:
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- 47.
Ako su P(A) i P(B) verovatnoce dva nezavisna dogadjaja A i B, onda verovatnoca da se nece realizovati oba dogadjaja:
- A.
P(A) * P(B)
- B.
(1-P(A)) * (1-P(B))
- C.
P(A) * (1-P(B))
- D.
(1-P(A)) * P(B)
Correct Answer
B. (1-P(A)) * (1-P(B))Explanation
The given correct answer (1-P(A)) * (1-P(B)) represents the probability that both events A and B will not occur. This can be derived from the fact that the probability of an event not occurring is equal to 1 minus the probability of it occurring. Since A and B are independent events, the probability of both not occurring can be calculated by multiplying the probabilities of each event not occurring, which gives (1-P(A)) * (1-P(B)).Rate this question:
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- 48.
Ako su P(A) i P(B) verovatnoce dva nezavisna dogadjaja A i B, onda je verovatnoca da se nece ralizovati dogadjaj A, hoce dogadjaj B:
- A.
P(A) * P(B)
- B.
(1-P(A)) * (1-P(B))
- C.
P(A) * (1-P(B))
- D.
(1-P(A)) * P(B)
Correct Answer
D. (1-P(A)) * P(B)Explanation
The given answer, (1-P(A)) * P(B), is the correct explanation. It represents the probability that event A will not occur (1-P(A)), multiplied by the probability that event B will occur (P(B)). This is based on the assumption that events A and B are independent of each other.Rate this question:
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- 49.
Ako su P(A) i P(B) verovatnoce dva nezavisna dogadjaja A i B, onda je verovatnoca da se bar jedan od njih nece realizovati:
- A.
1-P(A) * P(B)
- B.
(1-P(A)) * (1-P(B))
- C.
P(A) * (1-P(B))
- D.
(1-P(A)) * P(B)
Correct Answer
A. 1-P(A) * P(B)Explanation
The correct answer is 1-P(A) * P(B). This is because the probability that at least one of the events A or B will not occur is equal to 1 minus the probability that both events A and B will occur.Rate this question:
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- 50.
Ako su P(A) i P(B) verovatnoce dva nezavisna dogadjaja A i B, onda je verovatnoca da ce se realizovati bar jedan dogadjaj:
- A.
P(A) * P(B)
- B.
1-(1-P(A)) * (1-P(B))
- C.
P(A) * (1-P(B))
- D.
(1-P(A)) * P(B)
Correct Answer
B. 1-(1-P(A)) * (1-P(B))Explanation
The given answer, 1-(1-P(A)) * (1-P(B)), is the correct formula to calculate the probability of at least one of the events A or B occurring. It is derived from the probability theory rule for the complement of an event. The complement of the event "neither A nor B occurs" is "at least one of A or B occurs." By subtracting the probability of the complement from 1, we get the probability of at least one of the events occurring.Rate this question:
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