Q: If events $$A$$ and $$B$$ are mutually exclusive, which formula correctly gives the probability that either $$A or$$ $$B$$ occurs?

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

Q: Which formula should be used to find the probability of the union of two events that are NOT mutually exclusive?

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

Question 1

Which of the following pairs of events are mutually exclusive?

Accepted Answer

Rolling a 3 on a die and rolling a 4 on a die.

Question 2

If events $$A$$ and $$B$$ are mutually exclusive, which formula correctly gives the probability that either $$A or$$ $$B$$ occurs?

Accepted Answer

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

Question 3

A card is drawn from a standard deck. What is the probability that the card is a 4 or an ace?

Accepted Answer

$$\frac{8}{52}$$

Question 4

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

Accepted Answer

$$\frac{4}{6}$$

Question 5

Which of the following is NOT a characteristic of mutually exclusive events?

Accepted Answer

They can both occur in a single trial.

Question 6

A blood donor is randomly selected. What is the probability that the donor has type O or type A blood, given the following totals: 184 type O, 164 type A, and 409 total donors?

Accepted Answer

$$\frac{348}{409}$$

Question 7

A blood donor is randomly selected. What is the probability that the donor has type B or is Rh-negative, given 45 type B, 65 Rh-negative, and 8 who are both, out of 409 donors?

Accepted Answer

$$\frac{102}{409}$$

Question 8

Which formula should be used to find the probability of the union of two events that are NOT mutually exclusive?

Accepted Answer

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

Question 9

A sales representative's monthly sales are categorized as follows: 7 months between $$75K and 99K$$, 9 months between $$100K and 124K$$, out of 36 months. What is the probability that next month’s sales will be between $$75K and 124K$$?

Accepted Answer

$$\frac{16}{36}$$

Question 10

Suppose you randomly select a student. Event A: The student is a male. Event B: The student is a nursing major. Are these events mutually exclusive?

Accepted Answer

No, because a student can be both a male and a nursing major.

Question 11

If $$P(A) = 0.3$$, $$P(B) = 0.5$$, and $$P(A 	ext{ and } B) = 0.1$$, what is $$P(A 	ext{ or } B)$$?

Accepted Answer

$$0.7$$

Question 12

Which of the following real-life scenarios best illustrates the concept of mutually exclusive events?

Accepted Answer

A person can be born in either January or February, but not both.

Question 13

If two events are mutually exclusive, what is $$P(A 	ext{ and } B)$$?

Accepted Answer

$$0$$

Question 14

A die is rolled. Let $$A be $$the event 'rolling an even number' and $$B be $$the event 'rolling a number greater than 4'. What is $$P(A 	ext{ or } B)$$?

Accepted Answer

$$\frac{4}{6}$$

Question 15

Which of the following statements is true about the addition rule for probability?

Accepted Answer

It accounts for the overlap between two events when they are not mutually exclusive.

Probability and the Addition Rule: Mutually Exclusive Events

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