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

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

Q: Which formula represents the addition rule for three events A, B, and C?

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

Question 1

Which of the following best describes mutually exclusive events?

Accepted Answer

Two events that cannot occur at the same time.

Question 2

Suppose you roll a standard six-sided die. Let Event A be 'rolling a 3' and Event B be 'rolling a 4.' Are these events mutually exclusive?

Accepted Answer

Yes, because a die cannot show both 3 and 4 at the same time.

Question 3

A card is drawn from a standard deck of 52 cards. What is the probability that the card is a 4 or an ace? Use the addition rule for mutually exclusive events.

Accepted Answer

$$\frac{8}{52} \approx 0.154$$

Question 4

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

Accepted Answer

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

Question 5

You roll a die. What is the probability of rolling a number less than 3 or rolling an odd number?

Accepted Answer

$$\frac{4}{6} \approx 0.667$$

Question 6

A blood bank catalogs the types of blood given by donors. If a donor is selected at random, what is the probability the donor has type O or type A blood?

Accepted Answer

$$\frac{348}{409} \approx 0.851$$

Question 7

A sales representative’s monthly sales are recorded for 36 months. What is the probability that next month’s sales will be between $$75,000 and 124$$,999?

Accepted Answer

$$\frac{16}{36} \approx 0.444$$

Question 8

Which of the following is NOT an example of mutually exclusive events?

Accepted Answer

Selecting a card that is both a king and a queen.

Question 9

If $$P(A) = 0.3$$, $$P(B) = 0.5$$, and $$P(A 	ext{ and } B) = 0.2$$, what is $$P(A 	ext{ or } B)$$?

Accepted Answer

$$0.3 + 0.5 - 0.2 = 0.6$$

Question 10

A donor is selected at random from a blood bank. What is the probability the donor has type B blood or is Rh-negative? (Use the addition rule for non-mutually exclusive events.)

Accepted Answer

$$\frac{102}{409} \approx 0.249$$

Question 11

Which of the following scenarios describes events that are NOT mutually exclusive?

Accepted Answer

Selecting a student who is a male and a nursing major.

Question 12

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

Accepted Answer

$$0.4 + 0.3 = 0.7$$

Question 13

Which formula represents the addition rule for three events A, B, and C?

Accepted Answer

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

Question 14

A student is randomly selected from a university. Event A: The student is a public school teacher. Event B: The student is 25 years old. Are these events mutually exclusive?

Accepted Answer

No, because a student can be both a public school teacher and 25 years old.

Question 15

In a survey, 24.8% of the U.S. population is aged 45–64 years and 9.6% is aged 65–74 years. What is the probability that a randomly selected person is either 45–64 years or 65–74 years old, assuming these age groups are mutually exclusive?

Accepted Answer

$$24.8\% + 9.6\% = 34.4\%$$

Probability: The Addition Rule and Mutually Exclusive Events

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