Q: Which formula correctly expresses 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 statements about the Addition Rule is TRUE?

It requires subtracting $$P(A \text{ and } B) to $$avoid double-counting when events are not mutually exclusive.

Question 1

Which of the following pairs of events are mutually exclusive?

Accepted Answer

Selecting a 3 and selecting a 4 from a single roll of a die.

Question 2

Suppose you roll a standard six-sided die. Let event A be 'rolling a number less than 3' and event B be 'rolling an odd number.' What is $$P(A 	ext{ or } B)$$?

Accepted Answer

$$\dfrac{5}{6}$$

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?

Accepted Answer

$$\dfrac{8}{52}$$

Question 4

Which formula correctly expresses 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 survey of 10,121 adults found that 37% had trouble sleeping less than one day in the past week, and 30% had trouble sleeping one to two days. What is the probability that a randomly selected adult had trouble sleeping less than three days?

Accepted Answer

$$0.67$$

Question 6

A blood bank records the following: 184 donors have type O blood, 164 have type A, 45 have type B, and 16 have type AB. What is the probability that a randomly selected donor has type O or type A blood?

Accepted Answer

$$\dfrac{348}{409}$$

Question 7

In a frequency distribution of monthly sales, a sales representative had 7 months with sales between $$75,000 and 99$$,999, and 9 months with sales between $$100,000 and 124$$,999, out of 44 months total. What is the probability that next month’s sales will be between $$75,000 and 124$$,999?

Accepted Answer

$$\dfrac{16}{44}$$

Question 8

Which of the following statements about the Addition Rule is TRUE?

Accepted Answer

It requires subtracting $$P(A 	ext{ and } B) to $$avoid double-counting when events are not mutually exclusive.

Question 9

A draft pick in the NFL is randomly selected. There are 16 running backs and 37 wide receivers out of 255 total picks. What is the probability that the pick is NOT a running back or wide receiver?

Accepted Answer

$$1 - \dfrac{53}{255}$$

Question 10

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

Accepted Answer

Selecting a male student and selecting a nursing major.

Question 11

If $$P(A) = 0.4$$, $$P(B) = 0.3$$, and $$P(A 	ext{ and } B) = 0.1$$, what is $$P(A 	ext{ or } B)$$?

Accepted Answer

$$0.6$$

Question 12

A card is drawn from a standard deck. Let event A be 'drawing a jack' and event B be 'drawing a face card.' What is $$P(A 	ext{ and } B)$$?

Accepted Answer

$$\dfrac{4}{52}$$

Question 13

Which of the following best describes the complement of an event E?

Accepted Answer

All outcomes in the sample space not in E.

Question 14

A die is rolled. What is the probability of rolling a 6 or an odd number?

Accepted Answer

$$\dfrac{4}{6}$$

Question 15

Which of the following is NOT a valid probability value?

Accepted Answer

$$-0.2$$

Question 16

A blood donor is selected at random. What is the probability that the donor has type B blood or is Rh-negative, given 45 donors have type B, 65 are Rh-negative, and 409 donors in total, with 8 donors having both type B and Rh-negative?

Accepted Answer

$$\dfrac{45 + 65 - 8}{409}$$

Question 17

Which of the following best describes empirical probability?

Accepted Answer

Probability estimated from observed frequencies in experiments.

Question 18

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

Accepted Answer

$$0$$

Question 19

A card is drawn from a standard deck. What is the probability that the card is a face card or a heart? (There are 12 face cards and 13 hearts, with 3 cards being both face cards and hearts.)

Accepted Answer

$$\dfrac{12 + 13 - 3}{52}$$

Question 20

Which of the following is the correct interpretation of 'inclusive or' in probability?

Accepted Answer

A or B or both.

The Addition Rule and Mutually Exclusive Events in Probability

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