91Ó°ÊÓ

Suppose that \(25 \%\) of people have a dog, \(29 \%\) of people have a cat, and \(12 \%\) of people own both. What is the probability that someone owns a dog or a cat?

Forty-five percent of Americans like to cook and \(59 \%\) of Americans like to shop, while \(23 \%\) enjoy both activities. What is the probability that a randomly selected American either enjoys cooking or shopping or both?

A student figures that he has a \(30 \%\) chance of being let out of class late. If he leaves class late, there is a \(45 \%\) chance that he will miss his train. What is the probability that it will cause him to miss the train?

A nervous kicker usually makes \(70 \%\) of his first field goal attempts. If he makes his first attempt, his success rate rises to \(90 \%\). What is the probability that he makes his first two kicks?

On the Titanic, the probability of survival was \(0.323 .\) Among first- class passengers, it was \(0.625 .\) Were survival and ticket class independent? Explain.

If the sex of a child is independent of all other births, is the probability of a woman giving birth to a girl after having four boys greater than it was on her first birth? Explain.

A national survey indicated that \(30 \%\) of adults conduct their banking online. It also found that \(40 \%\) are younger than 50 , and that \(25 \%\) are younger than 50 and conduct their banking online. Make a probability table. Why is a table better than a tree here?

Suppose that the information in Exercise 9 had been presented in the following way. Facebook reports that \(70 \%\) of its users are from outside the United States. Of the U.S. users, two-thirds log on every day. Of the non-U.S. users, three-sevenths log on every day. Draw a tree for this situation. Why is the tree better than the table in this case? Where are the joint probabilities found?

Recent research suggests that \(73 \%\) of Americans have a home phone, \(83 \%\) have a cell phone, and \(58 \%\) of people have both. What is the probability that an American has a. a home or cell phone? b. neither a home phone nor a cell phone? c. a cell phone but no home phone?

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?