Q: Which formula correctly represents the Addition Rule for any two events A and B?

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

Q: Which of the following is NOT a correct application of the Addition Rule?

$$P(A \text{ or } B) = P(A) \times P(B)$$ for any two events

Question 1

Which of the following pairs of events are mutually exclusive?

Accepted Answer

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

Question 2

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

Accepted Answer

$$\frac{2}{3}$$

Question 3

A blood bank records the following donations: 120 type O, 100 type A, 45 type B, and 20 type AB. What is the probability that a randomly selected donor has type O or type A blood?

Accepted Answer

$$\frac{220}{285}$$

Question 4

Which formula correctly represents the Addition Rule for any two events A and B?

Accepted Answer

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

Question 5

A hospital records that 60 patients have type B blood, 80 are Rh-negative, and 15 have both type B and are Rh-negative. If there are 300 patients in total, what is the probability that a randomly selected patient has type B blood or is Rh-negative?

Accepted Answer

$$\frac{60 + 80 - 15}{300}$$

Question 6

If two events A and B are mutually exclusive, which of the following is always true?

Accepted Answer

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

Question 7

A company’s monthly sales are categorized as follows: $$25,000-49,999 (7 $$months), $$50,000-74,999 (9 $$months), $$75,000-99,999 (5 $$months), $$100,000-124,999 (8 $$months), $$125,000-149,999 (3 $$months), $$150,000-174,999 (2 $$months), $$175,000-199,999 (2 $$months). What is the probability that in a randomly selected month, sales were between $$25,000$$ and $$124,999$$?

Accepted Answer

$$\frac{7+9+5+8}{36}$$

Question 8

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

Accepted Answer

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

Question 9

Which of the following statements about the complement of an event E is correct?

Accepted Answer

$$P(E^c) = 1 - P(E)$$

Question 10

In a group of NFL rookies, 5 are running backs, 6 are wide receivers, and 14 play other positions. If one rookie is selected at random, what is the probability that the rookie is not a running back or wide receiver?

Accepted Answer

$$\frac{14}{25}$$

Question 11

A university has 200 male students, 150 nursing majors, and 30 male nursing majors. If a student is selected at random, what is the probability that the student is male or a nursing major?

Accepted Answer

$$\frac{200 + 150 - 30}{N}$$

Question 12

Which of the following is NOT a correct application of the Addition Rule?

Accepted Answer

$$P(A 	ext{ or } B) = P(A) 	imes P(B)$$ for any two events

Question 13

A blood bank has 120 type O donors, 100 type A donors, 45 type B donors, and 20 type AB donors. If 30 donors are Rh-negative, and 8 of those are type B and Rh-negative, what is the probability that a randomly selected donor is type B or Rh-negative?

Accepted Answer

$$\frac{45 + 30 - 8}{285}$$

Question 14

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

$$0.3 + 0.5 - 0.1 = 0.7$$

Question 15

Which of the following real-life scenarios describes two events that are NOT mutually exclusive?

Accepted Answer

Selecting a person who is left-handed and selecting a person who is a student.

Question 16

If the probability of event A is 0.4 and the probability of its complement is 0.6, what is the probability that either A or its complement occurs?

Accepted Answer

$$1$$

Question 17

A survey finds that 70 people like coffee, 50 like tea, and 20 like both. What is the probability that a randomly selected person likes coffee or tea, if there are 100 people surveyed?

Accepted Answer

$$\frac{70 + 50 - 20}{100}$$

Probability: The Addition Rule and Mutually Exclusive Events

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