Q: If events A and B are mutually exclusive, which formula correctly gives the probability of A or B occurring?

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

Q: Which formula should be used to find the probability of A or B when A and B 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

Selecting a person with blood type A and selecting a person with blood type O.

Question 2

If events A and B are mutually exclusive, which formula correctly gives the probability of A or B occurring?

Accepted Answer

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

Question 3

A blood bank records the blood types of donors. If 40 donors have type O, 30 have type A, and 10 have both type B and are Rh-negative, what is the probability that a randomly selected donor has type O or type A? (Assume there are 100 donors and no overlap between type O and type A.)

Accepted Answer

$$P = \frac{40 + 30}{100} = 0.70$$

Question 4

Which scenario best illustrates the use of the addition rule for non-mutually exclusive events?

Accepted Answer

Finding the probability of rolling a number less than 3 or an odd number on a die.

Question 5

A sales representative reached sales between $$75,000 and 124$$,999 in 8 out of 36 months. What is the probability that next month’s sales will fall in this range?

Accepted Answer

$$P = \frac{8}{36} = 0.222$$

Question 6

If you roll a die, what is the probability of rolling a number less than 3 or an odd number?

Accepted Answer

$$P = \frac{5}{6}$$

Question 7

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

Accepted Answer

They can be independent.

Question 8

A deck of 52 cards contains 4 aces and 4 fours. What is the probability of drawing a card that is a 4 or an ace?

Accepted Answer

$$P = \frac{8}{52} = \frac{2}{13}$$

Question 9

In a survey, 250 people voted 'Yes' on Issue 1, 180 voted 'Yes' on Issue 2, and 100 voted 'Yes' on both. What is the probability that a randomly selected person voted 'Yes' on Issue 1 or Issue 2?

Accepted Answer

$$P = \frac{250 + 180 - 100}{400} = 0.825$$

Question 10

Which formula should be used to find the probability of A or B when A and B are not mutually exclusive?

Accepted Answer

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

Question 11

A hospital records that 60 patients have blood type B, 40 are Rh-negative, and 15 have both. What is the probability that a randomly selected patient has blood type B or is Rh-negative? (There are 200 patients.)

Accepted Answer

$$P = \frac{60 + 40 - 15}{200} = 0.425$$

Question 12

Which of the following best describes the addition rule for probability?

Accepted Answer

It is used to find the probability that at least one of two events occurs.

Question 13

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

Accepted Answer

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

Question 14

A company tracks monthly sales. If the probability of reaching $$100,000 in sales is 0.25 and the probability of reaching 150$$,000 is 0.10, and these events are mutually exclusive, what is the probability of reaching either sales target?

Accepted Answer

$$P = 0.25 + 0.10 = 0.35$$

Probability and the Addition Rule: Mutually Exclusive and Joint Events

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