Q: Which formula correctly expresses the Special Addition Rule for two mutually exclusive events A and B?

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

Question 1

A fair die is rolled. What is the probability of rolling a number less than 5?

Accepted Answer

$$\frac{4}{6} = 0.6667$$

Question 2

If the probability of event A occurring is $$0.25$$, what is the probability of event A not occurring?

Accepted Answer

$$0.75$$

Question 3

A spinner has equal chances of landing on digits 0 through 9. What is the probability of landing on an odd number or a number greater than 7?

Accepted Answer

$$0.6$$

Question 4

In a population of flowers, 23% are white and 12% are yellow. If a flower is picked at random, what is the probability it can be used to make medicine (white or yellow)?

Accepted Answer

$$0.35$$

Question 5

Which of the following pairs of events are mutually exclusive?

Accepted Answer

Spending yesterday evening at home watching TV and going out clubbing yesterday evening

Question 6

A household is randomly selected from a town. The probability it has less than 4 people is given by:

Accepted Answer

$$P(1) + P(2) + P(3)$$

Question 7

If the probability of not A is $$0.4$$, what is the probability of A?

Accepted Answer

$$1 - 0.4 = 0.6$$

Question 8

Which formula correctly expresses the Special Addition Rule for two mutually exclusive events A and B?

Accepted Answer

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

Question 9

A spinner lands on digits 0–9. You win if you land on 0 or a number greater than 7. What is the probability of winning?

Accepted Answer

$$0.3$$

Question 10

Why can't the Special Addition Rule be used for events that are not mutually exclusive?

Accepted Answer

Because it would count overlapping outcomes twice

Question 11

If three events A, B, and C are mutually exclusive, what is the probability that at least one occurs?

Accepted Answer

$$P(A) + P(B) + P(C)$$

Question 12

A fair die is rolled. What is the probability of not rolling a 5?

Accepted Answer

$$1 - 0.1667 = 0.8333$$

Question 13

In a game, you win if you land on 3, a number greater than 7, or an even number. Are these events mutually exclusive?

Accepted Answer

No, because some outcomes can satisfy more than one event

Question 14

A household is randomly selected. What is the probability it has 1 or 2 people, given the relative frequencies are $$0.083$$ and $$0.140$$?

Accepted Answer

$$0.083 + 0.140 = 0.223$$

Question 15

If the probability of event B is $$0.3333$$, what is the probability of not B?

Accepted Answer

$$1 - 0.3333 = 0.6667$$

Question 16

Which of the following best describes mutually exclusive events?

Accepted Answer

Events that cannot happen simultaneously

Question 17

A spinner lands on digits 0–9. What is the probability of landing on a number greater than 7?

Accepted Answer

$$\frac{2}{10} = 0.2$$

Question 18

If the probability of event A is $$0.4$$ and event B is $$0.3$$, and they are mutually exclusive, what is the probability of A or B?

Accepted Answer

$$0.4 + 0.3 = 0.7$$

Question 19

A fair die is rolled. What is the probability of rolling a number greater than 4?

Accepted Answer

$$\frac{2}{6} = 0.3333$$

Question 20

Which of the following is an example of using the complement rule?

Accepted Answer

Calculating the probability of not raining by subtracting the probability of rain from 1

Rules of Probability: Complement and Addition Rules

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