Q: Which formula correctly expresses the addition rule for any two events A and B?

$$P(A \text{ or } B) = P(A) + P(B) - P(A \text{ and } B)$$

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

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

Accepted Answer

$$0.9$$

Question 3

Events A and B are disjoint. If $$P(A) = 0.3$$ and $$P(B) = 0.4$$, what is $$P(A 	ext{ or } B)$$?

Accepted Answer

$$0.7$$

Question 4

A survey finds that the probability a randomly selected household 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 5

Which formula correctly expresses the addition rule for any two events A and B?

Accepted Answer

$$P(A 	ext{ or } B) = P(A) + P(B) - P(A 	ext{ and } B)$$

Question 6

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

Accepted Answer

The occurrence of one event does not affect the probability of the other.

Question 7

A drug test has 45 positive and 5 negative results out of 50 subjects. If two subjects are selected with replacement, what is the probability the first is positive and the second is negative?

Accepted Answer

$$0.09$$

Question 8

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

$$0.999$$

Question 9

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

Accepted Answer

Selecting a person who is a male and a person who is a female.

Question 10

If $$P(A) = 0.6$$, what is $$P(\overline{A}) ($$the probability that event A does NOT occur)?

Accepted Answer

$$0.4$$

Question 11

Three employees are randomly selected without replacement from a population of 130,639,273, where the probability of a positive drug test is $$0.042. $$Using the 5% guideline, what is the probability all three test positive?

Accepted Answer

$$0.0000741$$

Question 12

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.

Question 13

If $$P(A) = 0.3$$ and $$P(B|A) = 0.5$$, what is $$P(A 	ext{ and } B)$$?

Accepted Answer

$$0.15$$

Question 14

Which of the following is a correct interpretation of the multiplication rule for two events A and B?

Accepted Answer

Multiply $$P(A) by$$ $$P(B|A)$$, where $$P(B|A) is $$the probability of B given A has occurred.

Question 15

A system uses redundancy by having two independent backup components, each with a failure probability of $$0.05. $$What is the probability that both components fail?

Accepted Answer

$$0.0025$$

Question 16

Which of the following statements is TRUE about mutually exclusive events?

Accepted Answer

They cannot occur at the same time.

Question 17

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

Accepted Answer

$$0.35$$

Question 18

A clinical trial randomly selects a participant. Event A is 'the participant is a male,' and event B is 'the participant is a female.' What is $$P(A 	ext{ and } B)$$?

Accepted Answer

$$0$$

Question 19

Which of the following is the correct formula for the probability of the complement of event A?

Accepted Answer

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

Question 20

Which of the following real-world examples best illustrates the principle of redundancy in probability?

Accepted Answer

Two independent hard drives in a computer system.

Probability: Addition and Multiplication Rules in Elementary Statistics

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