Q: Which of the following best describes the Addition Rule for disjoint (mutually exclusive) events?

If two events E and F are disjoint, then $$P(E \text{ or } F) = P(E) + P(F)$$

Q: Suppose a bag contains chips labeled 0 through 9. What is the probability of randomly selecting a chip labeled 3 or 5?

$$P(3 \text{ or } 5) = \frac{1}{10} + \frac{1}{10} = 0.2$$

Q: Given the probabilities for the first digit in Benford's Law, what is the probability that a randomly selected number begins with 1 or 2?

$$P(1 \text{ or } 2) = 0.301 + 0.176 = 0.477$$

Q: If three events E, F, and G are pairwise disjoint, what is the probability that at least one occurs?

$$P(E \text{ or } F \text{ or } G) = P(E) + P(F) + P(G)$$

Q: A card is drawn from a standard deck. What is the probability it is a king, queen, or jack?

$$P(\text{king or queen or jack}) = \frac{4}{52} + \frac{4}{52} + \frac{4}{52} = \frac{12}{52} = \frac{3}{13}$$

Q: Which formula represents the General Addition Rule for any two events E and F?

$$P(E \text{ or } F) = P(E) + P(F) - P(E \text{ and } F)$$

Q: A card is drawn from a standard deck. What is the probability it is a king or a diamond?

$$P(\text{king or diamond}) = \frac{4}{52} + \frac{13}{52} - \frac{1}{52} = \frac{16}{52} = \frac{4}{13}$$

Q: Using the complement rule, what is the probability that a randomly selected American has NOT played a state lottery if 52% have played?

$$P(\text{not played}) = 1 - 0.52 = 0.48$$

Q: If the probability of a household earning $$200,000 or more is 0.069, what is the probability of earning less than 200$$,000?

$$P(\text{less than } 200,000) = 1 - 0.069 = 0.931$$

Question 1

Which of the following best describes the Addition Rule for disjoint (mutually exclusive) events?

Accepted Answer

If two events E and F are disjoint, then $$P(E 	ext{ or } F) = P(E) + P(F)$$

Question 2

Suppose a bag contains chips labeled 0 through 9. What is the probability of randomly selecting a chip labeled 3 or 5?

Accepted Answer

$$P(3 	ext{ or } 5) = \frac{1}{10} + \frac{1}{10} = 0.2$$

Question 3

Which statement about mutually exclusive (disjoint) events is correct?

Accepted Answer

Mutually exclusive events have no outcomes in common.

Question 4

Given the probabilities for the first digit in Benford's Law, what is the probability that a randomly selected number begins with 1 or 2?

Accepted Answer

$$P(1 	ext{ or } 2) = 0.301 + 0.176 = 0.477$$

Question 5

If three events E, F, and G are pairwise disjoint, what is the probability that at least one occurs?

Accepted Answer

$$P(E 	ext{ or } F 	ext{ or } G) = P(E) + P(F) + P(G)$$

Question 6

A card is drawn from a standard deck. What is the probability it is a king, queen, or jack?

Accepted Answer

$$P(	ext{king or queen or jack}) = \frac{4}{52} + \frac{4}{52} + \frac{4}{52} = \frac{12}{52} = \frac{3}{13}$$

Question 7

Which formula represents the General Addition Rule for any two events E and F?

Accepted Answer

$$P(E 	ext{ or } F) = P(E) + P(F) - P(E 	ext{ and } F)$$

Question 8

A card is drawn from a standard deck. What is the probability it is a king or a diamond?

Accepted Answer

$$P(	ext{king or diamond}) = \frac{4}{52} + \frac{13}{52} - \frac{1}{52} = \frac{16}{52} = \frac{4}{13}$$

Question 9

Using the complement rule, what is the probability that a randomly selected American has NOT played a state lottery if 52% have played?

Accepted Answer

$$P(	ext{not played}) = 1 - 0.52 = 0.48$$

Question 10

If the probability of a household earning $$200,000 or more is 0.069, what is the probability of earning less than 200$$,000?

Accepted Answer

$$P(	ext{less than } 200,000) = 1 - 0.069 = 0.931$$

Question 11

In a contingency table, if there are 126.9 million males and 260.1 million total residents, what is the probability a randomly selected resident is male?

Accepted Answer

$$P(	ext{male}) = \frac{126.9}{260.1} \approx 0.488$$

Question 12

If 7804 thousand households earned less than $$10,000 out of 120,063 thousand total, what is the probability a household earned at least 10$$,000?

Accepted Answer

$$P(	ext{at least } 10,000) = 1 - \frac{7804}{120,063} \approx 0.935$$

Question 13

Which of the following is the correct definition of the complement of an event E?

Accepted Answer

The complement of E is all outcomes in the sample space S that are not outcomes in E.

Question 14

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

Accepted Answer

$$P(E^C) = 1 - 0.3 = 0.7$$

Question 15

In a contingency table, if the probability of being widowed is $$0.058$$ and divorced is $$0.109$$, what is the probability of being widowed or divorced?

Accepted Answer

$$P(	ext{widowed or divorced}) = 0.058 + 0.109 = 0.167$$

Question 16

If the probability of being male is $$0.488$$, widowed is $$0.058$$, and male and widowed is $$0.013$$, what is the probability of being male or widowed?

Accepted Answer

$$P(	ext{male or widowed}) = 0.488 + 0.058 - 0.013 = 0.533$$

The Addition Rule and Complements in Probability

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