Basic Probability Concept Questions!

1) Events are independent if the occurrence of one event does not affect the probability of the other.

True

False

The statement is true because when two events are independent, the probability of one event occurring does not change based on whether or not the other event occurs. In other words, the outcome of one event does not provide any information or influence the likelihood of the other event happening. This concept is fundamental in probability theory and is used to calculate the probability of multiple independent events occurring together.

Explanation

The statement is true because when two events are independent, the probability of one event occurring does not change based on whether or not the other event occurs. In other words, the outcome of one event does not provide any information or influence the likelihood of the other event happening. This concept is fundamental in probability theory and is used to calculate the probability of multiple independent events occurring together.

2) If P(A) > P(B), then event A is more likely to occur then event B.

True

False

If P(A) > P(B), it means that the probability of event A occurring is higher than the probability of event B occurring. Therefore, event A is more likely to occur than event B.

Explanation

If P(A) > P(B), it means that the probability of event A occurring is higher than the probability of event B occurring. Therefore, event A is more likely to occur than event B.

3) Is [your statement here] true or false?

True

False

The given answer is "True". This means that the statement mentioned in the question is true.

Explanation

The given answer is "True". This means that the statement mentioned in the question is true.

4) Is the statement "the larger sample size or more often you do an experiment, the closer your results will represent the entire population or predicted theoretical number" true or false?

True

False

The statement is true. Increasing the sample size or conducting the experiment more often helps to reduce the impact of random variation and provides a more accurate representation of the entire population or predicted theoretical number. With a larger sample size, the results are more likely to reflect the true characteristics of the population, increasing the reliability and validity of the findings. Additionally, conducting the experiment multiple times allows for the identification and elimination of outliers or anomalous results, leading to more consistent and accurate outcomes.

Explanation

The statement is true. Increasing the sample size or conducting the experiment more often helps to reduce the impact of random variation and provides a more accurate representation of the entire population or predicted theoretical number. With a larger sample size, the results are more likely to reflect the true characteristics of the population, increasing the reliability and validity of the findings. Additionally, conducting the experiment multiple times allows for the identification and elimination of outliers or anomalous results, leading to more consistent and accurate outcomes.

5) On a game show, the game that a contestant plays is chosen by spinning a spinner. The spinner has 5 colors on it: red, green, blue, purple, and orange. What is the complement of spinning a red or orange on this spinner? (Remember: complement = NOT)

Purple

Red, green, purple, orange, blue

Green, purple, blue

The complement of spinning a red or orange on the spinner would be the colors that are not red or orange. Therefore, the answer is green, purple, and blue, as these are the colors that are not red or orange.

Explanation

The complement of spinning a red or orange on the spinner would be the colors that are not red or orange. Therefore, the answer is green, purple, and blue, as these are the colors that are not red or orange.

6) If a month is picked at random, what is the probability that the month will start with M?

1/12

1/6

2/6

4/12

The probability that a month will start with M is 1 out of 6 because there are 12 months in a year and only 2 of them start with the letter M (March and May). Therefore, the probability is 1/6.

Explanation

The probability that a month will start with M is 1 out of 6 because there are 12 months in a year and only 2 of them start with the letter M (March and May). Therefore, the probability is 1/6.

7) Match the following events and their probabilities

Choosing a spade out of a normal pack of 52 playing cards

Rolling an even number of a normal die

Rolling a number between 1 and 6 on a normal die

Drawing a yellow marble out of a bag with blue and red marbles

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8) There are 20 marbles in a bag, 4 blue, 4 green, 4 red, 4 white and 4 black. Remember that all fraction answers should be given in the simplest form. What is the probability of drawing a black or white marble?

2/3

8/12

8/20

2/5

The probability of drawing a black or white marble can be found by adding the number of black marbles and white marbles and dividing it by the total number of marbles. In this case, there are 4 black marbles and 4 white marbles, so the sum is 8. The total number of marbles is 20. Therefore, the probability is 8/20, which can be simplified to 2/5.

Explanation

The probability of drawing a black or white marble can be found by adding the number of black marbles and white marbles and dividing it by the total number of marbles. In this case, there are 4 black marbles and 4 white marbles, so the sum is 8. The total number of marbles is 20. Therefore, the probability is 8/20, which can be simplified to 2/5.

9) Which of the following formulas is used to find the probability of rolling a 2 or landing on tails?

P(A) x P(B)

P(A) + P(B)

P(A) x P(B/A)

P(B/A)

The correct answer is P(A) x P(B). This formula is used to find the probability of two independent events occurring together. In this case, P(A) represents the probability of rolling a 2 and P(B) represents the probability of landing on tails. By multiplying these probabilities together, we can determine the probability of both events happening simultaneously.

Explanation

The correct answer is P(A) x P(B). This formula is used to find the probability of two independent events occurring together. In this case, P(A) represents the probability of rolling a 2 and P(B) represents the probability of landing on tails. By multiplying these probabilities together, we can determine the probability of both events happening simultaneously.

10) Match the following:

Probability

Outcome

Event

Sample space

Equally likely outcomes

Theoretical probability

Complement

Geometric probability

Experimental probability

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11) In a group of 100 people, 19 were drinking punch and 23 were eating fish. Find the probability that a person picked from this group at random is either eating fish or drinking punch.

The probability that a person picked at random from the group is either eating fish or drinking punch can be found by adding the probabilities of these two events occurring separately. Since there are 19 people drinking punch and 23 people eating fish, the total number of people who are either eating fish or drinking punch is 19 + 23 = 42. Therefore, the probability is 42/100 = 0.42 or 42%.

Explanation

The probability that a person picked at random from the group is either eating fish or drinking punch can be found by adding the probabilities of these two events occurring separately. Since there are 19 people drinking punch and 23 people eating fish, the total number of people who are either eating fish or drinking punch is 19 + 23 = 42. Therefore, the probability is 42/100 = 0.42 or 42%.

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