Probability Tester
This exercise is going to be pre training test to gauge what each of your understanding of probability is. The scores will then be compared with the scores of the post training test to determine how effective the session has been for each one of you.
You have 30 mins to complete the test beyond which the scores will not be considered.
Questions and Answers
- 1.
Suppose E is an event in a sample space S with probability .3. What is the probability of the complement of E?
- A.
1
- B.
.3
- C.
.7
- D.
0
Correct Answer
C. .7 -
- 2.
Suppose E and F are events in a sample space S. Suppose further that E has probability .5, F has probability .6, and the intersection of E and F has probability .2. Find the probability of the union of E and (the complement of F)
- A.
.6
- B.
.8
- C.
.3
- D.
.5
Correct Answer
A. .6 -
- 3.
Two six-sided dice are rolled. Find the probability that the sum is 8 given that the first die was 3.
- A.
1/5
- B.
1/6
- C.
5/18
- D.
1/12
Correct Answer
B. 1/6 -
- 4.
Two six-sided dice are rolled. But this time, the dice aren't fair: For each die, a 1 is twice as likely to be rolled as a 2, a 2 is twice as likely to be rolled as a 3, ..., and a 5 is twice as likely to be rolled as a 6 (in other words, each number is twice as likely as the number that follows it). So what is the probability of rolling a sum of 7?
- A.
64/1023
- B.
64/1223
- C.
64/1323
- D.
64/1123
Correct Answer
C. 64/1323 -
- 5.
We're playing poker with a standard pack of fifty-two cards without jokers. You have two pairs: 3, 3, 4, 4, 8. You are unaware of which cards the other players are holding. You decide to replace the 8 by another card from the pack. How do you rate your chances to turn your hand into a full house? (Full house means one trio and one pair.)
- A.
1/26
- B.
1/13
- C.
4/47
- D.
2/13
Correct Answer
C. 4/47 -
- 6.
Eight cardboard boxes are standing on the table. Two among them contain a present, the other six are empty. You are allowed to open two boxes. How much chance do you have to find at least one present?
- A.
7/16
- B.
9/16
- C.
15/28
- D.
13/28
Correct Answer
D. 13/28 -
- 7.
A game show requires you to randomly pick 1 of 6 envelopes. The host has hidden a $100 bill in one envelope, and a $1 bill in each of the other 5. Once you've picked, the host is required to remove 2 $1 envelopes you didn't pick. You now have a choice of keeping your original envelope, or paying $2 to switch your choice to one of the 3 you didn't pick. If you choose to pay $2 and switch your choice, then what are your odds of losing money?
- A.
2/3
- B.
11/16
- C.
13/18
- D.
3/4
Correct Answer
C. 13/18 -
- 8.
A study has been done to determine whether or not a certain drug leads to an improvement in symptoms for patients with a particular medical condition. The results are shown in the following table.ImprovementNo ImprovementTotalDrug270530800No Drug120280400Total3908101200Based on this table, what is the (empirical) probability that a patient shows improvement if it is known that the patient was given the drug?
- A.
None of the answers given
- B.
.225
- C.
.3375
- D.
.325
Correct Answer
C. .3375Explanation
The empirical probability can be calculated by dividing the number of patients who showed improvement after taking the drug by the total number of patients who were given the drug. In this case, the number of patients who showed improvement after taking the drug is 270, and the total number of patients given the drug is 800. Therefore, the empirical probability is 270/800 = 0.3375, which can be expressed as 0.3375 or 33.75%.Rate this question:
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- 9.
The results of the study in question #9 on the relationship between a certain drug and the improvement in symptoms for patients with a particular medical conditon are repeated below. ImprovementNo ImprovementTotalDrug270530800No Drug120280400Total3908101200Based on this table, are the events "has the drug" and "improvement" independent events?
- A.
No, they are not independent
- B.
Yes, they are independent
Correct Answer
A. No, they are not independentExplanation
The table shows the number of patients who have taken the drug and whether they experienced improvement or not. To determine if the events "has the drug" and "improvement" are independent, we need to compare the observed frequencies with the expected frequencies under independence. If the observed frequencies are significantly different from the expected frequencies, then the events are not independent. In this case, the observed frequencies are not equal to the expected frequencies, indicating that the events are not independent. Therefore, the correct answer is "No, they are not independent."Rate this question:
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- 10.
A company has three plants at which it produces a certain item. 30% are produced at Plant A, 50% at Plant B, and 20% at Plant C. Suppose that 1%, 4% and 3% of the items produced at Plants A, B and C respectively are defective. If an item is selected at random from all those produced, what is the probability that the item was produced at Plant B and is defective?
- A.
.02
- B.
None of the answers given
- C.
.2
- D.
.04
Correct Answer
A. .02Explanation
The probability that an item was produced at Plant B and is defective can be calculated by multiplying the probability of being produced at Plant B (50%) with the probability of being defective at Plant B (4%). This gives us 0.5 * 0.04 = 0.02, which is equal to .02.Rate this question:
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- 11.
In a group of 339 people, at least two of them have the same first-name and last-name initials, possibly switched (as in Constance Smith and Selwyn Crown)
- A.
True
- B.
False
Correct Answer
B. FalseExplanation
In a group of 339 people, it is not guaranteed that at least two of them will have the same first-name and last-name initials, possibly switched. It is possible that all 339 people have unique initials or that some initials are repeated but not switched. Therefore, the statement is false.Rate this question:
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Our quizzes are rigorously reviewed, monitored and continuously updated by our expert board to maintain accuracy, relevance, and timeliness.
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Current Version
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Mar 21, 2023Quiz Edited by
ProProfs Editorial Team -
Jan 13, 2009Quiz Created by
Tedelweiss
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