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Magazine Problem 18
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 25
You are dealt a hand of three cards, one at a time. Find the probability of each of the following. a) The first heart you get is the third card dealt. b) Your cards are all red (that is, all diamonds or hearts). c) You get no spades. d) You have at least one ace.
Problem 34
The local animal shelter in Exercise 18 reported that it currently has 24 dogs and 18 cats available for adoption; 8 of the dogs and 6 of the cats are male. Are the species and sex of the animals independent? Explain.
Problem 43
Leah is flying from Boston to Denver with a connection in Chicago. The probability her first flight leaves on time is \(0.15 .\) If the flight is on time, the probability that her luggage will make the connecting flight in Chicago is \(0.95,\) but if the first flight is delayed, the probability that the luggage will make it is only 0.65. a) Are the first flight leaving on time and the luggage making the connection independent events? Explain. b) What is the probability that her luggage arrives in Denver with her?
Problem 52
An airline offers discounted "advancepurchase" fares to customers who buy tickets more than 30 days before travel and charges "regular" fares for tickets purchased during those last 30 days. The company has noticed that \(60 \%\) of its customers take advantage of the advance-purchase fares. The "no-show" rate among people who paid regular fares is \(30 \%,\) but only \(5 \%\) of customers with advance- purchase tickets are no-shows. a) What percent of all ticket holders are no-shows? b) What's the probability that a customer who didn't show had an advance- purchase ticket? c) Is being a no-show independent of the type of ticket a passenger holds? Explain.
