Chapter 7 Review Problems

Problem #1 Use a Venn diagram and the given information to determine the number of elements in the indicated region. n(A) = 35, n(B)= 18, n(A  B) = 45, n(B) = 43 n(A) = 35, n(B)= 18, n(A  B) = 45, n(B) = 43 Find n(A  B) Find n(A  B)

Problem #2 Use a Venn diagram to find the indicated probability. P(R) = 0.39, P(S) = 0.34, P(R  S) = 0.21 P(R) = 0.39, P(S) = 0.34, P(R  S) = 0.21 Find P(R  S) Find P(R  S)

Problem #3 A card is drawn from a well-shuffled deck of 52 cards. What is the probability of drawing a red card that has a value greater than 5? (Assume Aces are high.)

Problem #4 The age distribution of students at a community college is given below. Age (years) Number of Students Under – – – Over A student is selected at random. Find the probability that the student is at most 25 years old. Round to the nearest thousandth. A student is selected at random. Find the probability that the student is at most 25 years old. Round to the nearest thousandth.

Problem #5 The odds in favor of a football team winning the Super Bowl are posted as 6:5. Find the probability that the team will lose the Super Bowl.

Problem #6 Assume that two gumballs are chosen from a bag of gumballs with 4 blue, 1 white, 3 green, and 3 red. Find the probability that: a.) both gumballs are blue. b.) the first gumball is red and the second gumball is green. gumball is green.

Problem #7 In a certain U.S. city, 54.9% of adults are women. In that city, 16.2% of women and 10.2% of men do not use any means of public transportation. If an adult is selected at random from the city, find the probability that the person does not use any form of public transportation.

Problem #8 A card is drawn from a well-shuffled deck of 52 cards. Let A be the event that the card is a spade. Let B be the event that the card is a ten. Find: P(A) P(B) P(B) P(A  B) P(A  B) Are events A and B independent? Are events A and B independent? How can you tell? How can you tell?

Problem #9 A person must select one of three bags, each filled with pennies. One bag contains a gold coin. The probability of bag A being selected is 0.35, while the probability of bag B being selected is The probability of finding a gold coin in bag A is 0.3,in bag B is 0.45, and in bag C is 0.8. A bag is selected at random. a.) Draw a tree diagram and label each branch with the appropriate probabilities. the appropriate probabilities. b.) What is the probability of getting the gold coin? c.) Given that a person got the gold coin, what is the probability that bag C contained the coin? probability that bag C contained the coin?

Problem #10 A survey of 200 families showed that 98 had a dog; 57 had a cat; 20 had a dog and a cat; 51 had neither a dog nor a cat nor a parakeet; and 2 had a cat, a dog, and a parakeet. How many families had a parakeet only? How many families had a parakeet only?

Answers 1.) 53 2.) ) 9/26 or ) ) 5/11 6.) a.) 6/55 or b.) 9/110 or ) ) P(A) = ¼P(B) = 1/13 P(A  B) = 1/52Independent events P(A  B) = 1/52Independent events Because P(A) P(B) = P(A  B) Because P(A) P(B) = P(A  B) 9.) b.) 0.527c.) ) 14