Problem 1
Real estate ads suggest that \(64 \%\) of homes for sale have garages, \(21 \%\) have swimming pools, and \(17 \%\) have both features. What is the probability that a home for sale has a) a pool or a garage? b) neither a pool nor a garage? c) a pool but no garage?
Problem 2
Suppose the probability that a U.S. resident has traveled to Canada is \(0.18\), to Mexico is \(0.09\), and to both countries is 0.04. What's the probability that an American chosen at random has a) traveled to Canada but not Mexico? b) traveled to either Canada or Mexico? c) not traveled to either country?
Problem 3
a check of dorm rooms on a large college campus revealed that \(38 \%\) had refrigerators, \(52 \%\) had TVs, and \(21 \%\) had both a TV and a refrigerator. What's the probability that a randomly selected dorm room has a) a TV but no refrigerator? b) a TV or a refrigerator, but not both? c) neither a TV nor a refrigerator?
Problem 4
Employment data at a large company reveal that \(72 \%\) of the workers are married, that \(44 \%\) are college graduates, and that half of the college grads are married. What's the probability that a randomly chosen worker a) is neither married nor a college graduate? b) is married but not a college graduate? c) is married or a college graduate?
Problem 7
You draw a card at random from a standard deck of 52 cards. Find each of the following conditional probabilities: a) The card is a heart, given that it is red. b) The card is red, given that it is a heart. c) The card is an ace, given that it is red. d) The card is a queen, given that it is a face card.
Problem 8
In its monthly report, the local animal shelter states that it currently has 24 dogs and 18 cats available for adoption. Eight of the dogs and 6 of the cats are male Find each of the following conditional probabilities if an animal is selected at random: a) The pet is male, given that it is a cat. b) The pet is a cat, given that it is female. c) The pet is female, given that it is a dog.
Problem 13
Seventy percent of kids who visit a doctor have a fever, and \(30 \%\) of kids with a fever have sore throats. What's the probability that a kid who goes to the doctor has a fever and a sore throat?
Problem 14
Twenty percent of cars that are inspected have faulty pollution control systems. The cost of repairing a pollution control system exceeds $$\$ 100$$ about \(40 \%\) of the time. When a driver takes her car in for inspection, what's the probability that she will end up paying more than $$\$ 100$$ to repair the pollution control system?
Problem 16
You pick three cards at random from a deck. Find the probability of each event described below. a) You get no aces. b) You get all hearts. c) The third card is your first red card. d) You have at least one diamond.
Problem 17
A junk box in your room contains a dozen old batteries, five of which are totally dead. You start picking batteries one at a time and testing them. Find the probability of each outcome. a) The first two you choose are both good. b) At least one of the first three works. c) The first four you pick all work. d) You have to pick 5 batteries to find one that works.
