9.2

Two cards are drawn without replacement from a standard deck of 52 playing cards. What is the probability of choosing a club and then, without replacement, another club? Express your answer as a fraction or a decimal number rounded to four decimal places.

Answer: 1/17 Explanation: 13/52 * 12/51

You have a container with balls numbered between 1 and 20. If you randomly draw a ball from the container, what is the probability that the number on the ball will be divisible by three or will have a value three through eight?

Answer: 1/2 Explanation: - P(divisible by 3): = 6/20 - P(have a value 3 through 8): = 6/20 - P(divisible by 3 and have a value 3 through 8) = 2/20 Since the events are not mutually exclusive, use the addition rule for non-mutually exclusive events, P(A or B) = P(A)+P(B) − P(A and B), to calculate P(divisible by 3 or have a value three through eight).

Suppose we select a card from a deck of playing cards. What is the probability of drawing a diamond or drawing a face card? (The face cards are the jack, queen, and king.) P(A or B) = P(A) + P(B) − P(A and B)

Answer: 11/26 Explanation: Because the events are not mutually exclusive, we need to use the addition rule for non-mutually exclusive events, P(A or B) = P(A) + P(B) − P(A and B) P(A) = P(drawing a diamond) = 13/52, since there are 13 diamonds in a deck of 52 cards. P(B) = P(drawing a face card) = 12/52, since there are 4 jacks, 4 queens, and 4 kings in a deck of 52 cards. P(A+B) = Intersection of A+B P(drawing a diamond and drawing a face card) = P(J♦Q♦K♦) = 3/52 P(A or B) = P(A) + P(B) − P(A and B) = P(drawing a diamond) + P(drawing a face card) − P(J♦Q♦K♦) = 13/52 + 12/52 − 3/52 = 22/52 = 11/26

If the odds against a horse winning a race is 7:12, what is the probability of the horse winning the race? Express your answer as a simplified fraction.

Answer: 12/19 Explanation: q/p+q

Find the probability of choosing a letter other than the letter G from a bag that contains the fifteen letters of the Indian city PALASA KASIBUGGA. Express your answer as a fraction in lowest terms or a decimal rounded to the nearest millionth.

Answer: 13/15 Explanation: Compliment rule

If the odds in favor of a horse winning a race is 5:6, what is the probability of the horse winning the race? Express your answer as a simplified fraction.

Answer: 5/11 Explanation: P(E) = p/p+q

If the odds in favor of a horse winning a race is 7:12, what is the probability of the horse winning the race? Express your answer as a simplified fraction.

Answer: 7/19 Explanation: P(E) = p/p+q