Q: Given events A and B are mutually exclusive, which formula correctly calculates $$P(A \text{ or } B)$$?

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

Q: A blood bank catalogs donors by blood type and Rh factor. If 156 donors have type O blood and 102 have type A blood out of 409 total donors, what is the probability that a randomly selected donor has type O or type A blood?

$$P(\text{O or A}) = \frac{156 + 102}{409}$$

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

$$P(\text{less than 3 or odd}) = \frac{2}{6} + \frac{3}{6} - \frac{1}{6} = \frac{4}{6}$$

Q: If events A and B are not mutually exclusive, which formula should be used to find $$P(A \text{ or } B)$$?

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

Q: A standard deck of 52 cards is used. What is the probability of drawing a 4 or an ace?

$$P(4 \text{ or } A) = \frac{4}{52} + \frac{4}{52} = \frac{8}{52}$$

Question 1

Which of the following pairs of events are mutually exclusive? 
A) Drawing a red card and drawing a king from a standard deck of cards. 
B) Rolling a 2 and rolling an even number on a six-sided die. 
C) Selecting a male student and selecting a nursing major. 
D) Drawing a heart and drawing a queen from a standard deck of cards.

Accepted Answer

D) Drawing a 4 and drawing an ace from a standard deck of cards.

Question 2

Given events A and B are mutually exclusive, which formula correctly calculates $$P(A 	ext{ or } B)$$?

Accepted Answer

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

Question 3

A blood bank catalogs donors by blood type and Rh factor. If 156 donors have type O blood and 102 have type A blood out of 409 total donors, what is the probability that a randomly selected donor has type O or type A blood?

Accepted Answer

$$P(	ext{O or A}) = \frac{156 + 102}{409}$$

Question 4

Which of the following best describes the Addition Rule for probability?

Accepted Answer

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

Question 5

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

Accepted Answer

$$P(	ext{less than 3 or odd}) = \frac{2}{6} + \frac{3}{6} - \frac{1}{6} = \frac{4}{6}$$

Question 6

Which of the following is NOT a property of probability?

Accepted Answer

The probability of an event can be greater than 1.

Question 7

A company tracks monthly sales. If the probability of sales between $$75,000 and 99$$,999 is $$\frac{11}{36}$$ and between $$100,000 and 124$$,999$$ is $$\frac{13}{36}$, what is the probability that next month’s sales will be in either range?

Accepted Answer

$$\frac{11}{36} + \frac{13}{36} = \frac{24}{36}$$

Question 8

If events A and B are not mutually exclusive, which formula should be used to find $$P(A 	ext{ or } B)$$?

Accepted Answer

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

Question 9

A standard deck of 52 cards is used. What is the probability of drawing a 4 or an ace?

Accepted Answer

$$P(4 	ext{ or } A) = \frac{4}{52} + \frac{4}{52} = \frac{8}{52}$$

Question 10

If the probability of selecting a running back in the NFL draft is $$\frac{29}{255}$$ and a wide receiver is $$\frac{24}{255}$$, what is the probability of selecting either a running back or a wide receiver?

Accepted Answer

$$\frac{29}{255} + \frac{24}{255} = \frac{53}{255}$$

Question 11

Which of the following is an example of empirical probability?

Accepted Answer

Estimating the probability of rain tomorrow based on weather data from the past month.

Question 12

If $$P(E) = 0.3$$, what is $$P(E')$$, the probability of the complement of E?

Accepted Answer

$$P(E') = 0.7$$

Question 13

A student is randomly selected from a university. Event A: The student is a freshman. Event B: The student is a biology major. Are these events mutually exclusive?

Accepted Answer

No, because a student can be both a freshman and a biology major.

Question 14

Which rule would you use to find the probability that a randomly selected NFL draft pick is NOT a running back or a wide receiver?

Accepted Answer

The complement rule: $$P(	ext{not } (A 	ext{ or } B)) = 1 - P(A 	ext{ or } B)$$

Question 15

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

$$P(A 	ext{ or } B) = 0.4 + 0.5 - 0.2 = 0.7$$

Addition Rule and Mutually Exclusive Events in Probability

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