Q: If two events A and B are independent, which of the following is true?

$$P(A \text{ and } B) = P(A) \times P(B)$$

Q: A bag contains 3 green, 4 blue, and 5 red marbles. If two marbles are drawn without replacement, what is the probability that both are blue?

$$\frac{4}{12} \times \frac{3}{11}$$

Q: Which of the following statements about conditional probability is correct?

$$P(B|A) = \frac{P(A \text{ and } B)}{P(A)}$$

Question 1

Which of the following best describes a simple event in probability?

Accepted Answer

An outcome that cannot be broken down into simpler components.

Question 2

A die is rolled once. What is the probability of getting an even number? (Assume a fair six-sided die.)

Accepted Answer

$$\frac{1}{2}$$

Question 3

If the probability of an event A is $$0.3$$, what is the probability of the complement of A?

Accepted Answer

$$0.7$$

Question 4

A bag contains 5 red balls and 7 blue balls. If one ball is drawn at random, what is the probability that it is blue? Express your answer as a decimal rounded to three significant digits.

Accepted Answer

$$0.583$$

Question 5

Which of the following is NOT a valid approach to finding probability?

Accepted Answer

Assuming all outcomes are equally likely without evidence

Question 6

A medical test for a disease has a true positive rate of $$0.90$$ and a false positive rate of $$0.05. If$$ $$2\% of $$the population has the disease, what is the probability that a randomly selected person who tests positive actually has the disease? (Use Bayes’ theorem.)

Accepted Answer

$$\frac{0.018}{0.067}$$

Question 7

If two events A and B are independent, which of the following is true?

Accepted Answer

$$P(A 	ext{ and } B) = P(A) 	imes P(B)$$

Question 8

A password consists of 4 digits, each from 0 to 9. What is the probability of guessing the correct password on the first try?

Accepted Answer

$$\frac{1}{10000}$$

Question 9

A committee of 3 people is to be chosen from a group of 8. How many different committees are possible?

Accepted Answer

$$\binom{8}{3}$$

Question 10

In a lottery, you must select 5 numbers from 1 to 39. What is the probability of winning if you buy one ticket? (Order does not matter.)

Accepted Answer

$$\frac{1}{575757}$$

Question 11

If $$P(A) = 0.4$$ and $$P(B) = 0.5$$, and A and B are mutually exclusive, what is $$P(A 	ext{ or } B)$$?

Accepted Answer

$$0.9$$

Question 12

A researcher must visit 5 different cities. In how many different orders can the cities be visited?

Accepted Answer

$$5!$$

Question 13

A survey finds that the probability a randomly selected person has sleepwalked is $$0.292. $$What is the probability that a randomly selected person has NOT sleepwalked?

Accepted Answer

$$0.708$$

Question 14

A bag contains 3 green, 4 blue, and 5 red marbles. If two marbles are drawn without replacement, what is the probability that both are blue?

Accepted Answer

$$\frac{4}{12} 	imes \frac{3}{11}$$

Question 15

Which of the following is the correct formula for the number of permutations of n items, where $$n_1$$ are alike, $$n_2$$ are alike, ..., $$n_k$$ are alike?

Accepted Answer

$$\frac{n!}{n_1$! n_2$! \ldots n_k!}$$

Question 16

A test for a virus has a 97% true positive rate and a 1% false positive rate. If 1 in 1000 people has the virus, what is the probability that a person who tests positive actually has the virus? (Use Bayes’ theorem.)

Accepted Answer

$$\frac{0.00097}{0.00097 + 0.00999}$$

Question 17

If $$P(A) = 0.3$$, $$P(B) = 0.4$$, and $$P(A 	ext{ and } B) = 0.1$$, what is $$P(A 	ext{ or } B)$$?

Accepted Answer

$$0.3 + 0.4 - 0.1 = 0.6$$

Question 18

A company finds that 6% of damaged iPads were damaged by bags/backpacks. If 20 damaged iPads are randomly selected, what is the probability that at least one was damaged in a bag/backpack?

Accepted Answer

$$1 - 0.94$$^{20}$$

Question 19

Which of the following statements about conditional probability is correct?

Accepted Answer

$$P(B|A) = \frac{P(A 	ext{ and } B)}{P(A)}$$

Chapter 4: Probability – Foundations and Applications in Statistics CHAP 4

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