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

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

Q: A bag contains 5 red balls and 7 blue balls. If two balls are drawn one after another without replacement, what is the probability both are red?

$$\frac{5}{12} \times \frac{4}{11}$$

Question 1

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

Accepted Answer

An event that combines two or more simple events.

Question 2

Suppose the probability that a randomly selected household in the U.S. has a smartphone is 0.87. What is the probability that a randomly selected household does NOT have a smartphone?

Accepted Answer

$$0.13$$

Question 3

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

Accepted Answer

$$P(A 	ext{ and } B) = 0$$

Question 4

A clinical trial randomly selects a participant. Let event A be 'the participant is male' and event B be 'the participant is female.' What is the relationship between A and B?

Accepted Answer

A and B are disjoint.

Question 5

Given $$P(A) = 0.4$$, $$P(B) = 0.5$$, and $$P(A 	ext{ and } B) = 0.2$$, what is $$P(A 	ext{ or } B)$$?

Accepted Answer

$$0.9$$

Question 6

Which formula correctly expresses the probability of the complement of event A?

Accepted Answer

$$P(\overline{A}) = 1 - P(A)$$

Question 7

A drug test yields a positive result with probability $$0.042. If $$three employees are randomly selected without replacement from a population of 130,639,273, what is the probability all three test positive? (Use the 5% guideline for cumbersome calculations.)

Accepted Answer

$$(0.042)^3 = 0.0000741$

Question 8

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

Accepted Answer

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

Question 9

A computer has two independent hard drives, each with a failure probability of $$0.0289 in a $$year. What is the probability that at least one hard drive does NOT fail in a year?

Accepted Answer

$$1 - (0.0289)^2$

Question 10

Which of the following statements about sampling is correct?

Accepted Answer

Sampling with replacement results in independent events.

Question 11

If $$P(A) = 0.6$$ and $$P(B|A) = 0.5$$, what is $$P(A 	ext{ and } B)$$?

Accepted Answer

$$0.3$$

Question 12

A system is designed with redundancy so that it will function as long as at least one of two independent components works. If each component has a probability of $$0.95 of $$working, what is the probability the system works?

Accepted Answer

$$1 - (1 - 0.95)^2$

Question 13

Which of the following is an example of mutually exclusive (disjoint) events?

Accepted Answer

Selecting a person who is either under 18 or over 65.

Question 14

If $$P(A) = 0.7$$ and $$P(B) = 0.5$$, and A and B are disjoint, what is $$P(A 	ext{ or } B)$$?

Accepted Answer

$$0.7 + 0.5 = 1.2$$

Question 15

A bag contains 5 red balls and 7 blue balls. If two balls are drawn one after another without replacement, what is the probability both are red?

Accepted Answer

$$\frac{5}{12} 	imes \frac{4}{11}$$

Question 16

Which of the following best describes the 5% guideline for cumbersome calculations?

Accepted Answer

If the sample size is no more than 5% of the population, treat dependent events as independent.

Probability: Addition and Multiplication Rules in Elementary Statistics

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