Q: What is the formal addition rule for the probability of A or B?

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

Q: Which of the following is the correct formal multiplication rule for the probability of A and B?

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

Q: If you select two drivers at random, what is the probability that both texted while driving? (Use the table: 731 + 3054 = 3785 texted while driving, total = 8505)

$$\frac{3785}{8505} \times \frac{3784}{8504}$$

Question 1

Which of the following best describes a compound event?

Accepted Answer

Any event combining two or more simple events.

Question 2

Events A and B are disjoint if:

Accepted Answer

They cannot occur at the same time.

Question 3

Given the table of drug test results, what is the probability that a randomly selected subject had a positive test result or uses drugs? (Total subjects = 555)

Accepted Answer

Question 4

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

Accepted Answer

The occurrence of A does not affect the probability of B.

Question 5

What is the formal addition rule for the probability of A or B?

Accepted Answer

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

Question 6

Suppose you randomly select two people from your class. What is the probability that both are born on Monday, assuming birthdays are equally likely on any day of the week?

Accepted Answer

$$\frac{1}{49}$$

Question 7

If you have 7 children, what is the probability that all are boys? (Assume probability of boy = 0.5 for each child)

Accepted Answer

$$\left(0.5\$$right)^7$$

Question 8

Using the high school driver table, what is the probability that a randomly selected driver texted while driving or drove when drinking alcohol?

Accepted Answer

Question 9

Which of the following is the correct formal multiplication rule for the probability of A and B?

Accepted Answer

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

Question 10

If you select three employees without replacement from a population of 130,639,273, and the probability of a positive drug test is 0.042, what guideline allows you to treat the selections as independent?

Accepted Answer

The 5% guideline for cumbersome calculations.

Question 11

Which of the following pairs of events are disjoint?

Accepted Answer

Getting a head and getting a tail in a single coin toss.

Question 12

If two events are not disjoint, which of the following must be true?

Accepted Answer

They have at least one outcome in common.

Question 13

A study finds that 97% of Americans own a smartphone. What percent do not own a smartphone?

Accepted Answer

3%

Question 14

If you randomly select two people from a group, what is the probability that they are both born on the same day of the week?

Accepted Answer

$$\frac{1}{7}$$

Question 15

Which of the following best describes independent events?

Accepted Answer

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

Question 16

If you select two drivers at random, what is the probability that both texted while driving? (Use the table: 731 + 3054 = 3785 texted while driving, total = 8505)

Accepted Answer

$$\frac{3785}{8505} 	imes \frac{3784}{8504}$$

Question 17

Which of the following is an example of dependent events?

Accepted Answer

Drawing two cards from a deck without replacement.

Question 18

If the probability of event A is 0.3 and the probability of event B is 0.4, and A and B are disjoint, what is $$P(A 	ext{ or } B)$$?

Accepted Answer

$$0.3 + 0.4 = 0.7$$

Question 19

If you select two people from a group of 50 drug users, what is the probability that the first has a positive test and the second has a negative test, with replacement? (45 positive, 5 negative)

Accepted Answer

$$\frac{45}{50} 	imes \frac{5}{50}$$

Question 20

If you select two people from a group of 50 drug users, what is the probability that the first has a positive test and the second has a negative test, without replacement? (45 positive, 5 negative)

Accepted Answer

$$\frac{45}{50} 	imes \frac{5}{49}$$

Probability Rules and Applications: Compound Events, Disjoint Events, and Multiplication Rule

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