91Ó°ÊÓ

Polling, part II According to Pew Research, the contact rate (probability of contacting a selected household) was \(90 \%\) in 1997 and \(62 \%\) in 2012 . However, the cooperation rate (probability of someone at the contacted household agreeing to be interviewed) was \(43 \%\) in 1997 and dropped to \(14 \%\) in \(2012 .\) a. What is the probability (in 2012 ) of obtaining an interview with the next household on the sample list? (To obtain an interview, an interviewer must both contact the household and then get agreement for the interview.) b. Was it more likely to obtain an interview from a randomly selected household in 1997 or in \(2012 ?\)

M\&M's The Mars company says that before the introduction of purple, yellow candies made up \(20 \%\) of their plain M\&M's, red another \(20 \%,\) and orange, blue, and green each made up \(10 \%\). The rest were brown. a. If you pick an M\&M at random, what is the probability that 1\. it is brown? 2\. it is yellow or orange? 3\. it is not green? 4\. it is striped? b. If you pick three M\&M's in a row, what is the probability ability that 1\. they are all brown? 2\. the third one is the first one that's red? 3\. none are yellow? 4\. at least one is green?

Blood The American Red Cross says that about \(45 \%\) of the U.S. population has Type O blood, \(40 \%\) Type A, \(11 \%\) Type B, and the rest Type \(\mathrm{AB}\). a. Someone volunteers to give blood. What is the probability that this donor 1\. has Type AB blood? 2\. has Type A or Type B? 3\. is not Type O? b. Among four potential donors, what is the probability that 1\. all are Type O? 2\. no one is Type AB? 3\. they are not all Type \(\mathrm{A}\) ? 4\. at least one person is Type B?

Disjoint or independent? In Exercise 40 ?, you calculated probabilities involving various blood types. Some of your answers depended on the assumption that the outcomes described were disjint; that is, they could not both happen at the same time. Other answers depended on the assumption that the events were independent; that is, the occurrence of one of them doesn't affect the probability of the other. Do you understand the difference between disjoint and independent? a. If you examine one person, are the events that the person is Type \(\mathrm{A}\) and that the same person is Type \(\mathrm{B}\) disjoint, independent, or neither? b. If you examine two people, are the events that the first is Type A and the second Type B disjoint, independent, or neither? c. Can disjoint events ever be independent? Explain.

Dice You roll a fair die three times. What is the probability that a. you roll all 6 's? b. you roll all odd numbers? C. none of your rolls gets a number divisible by \(3 ?\) d. you roll at least one \(5 ?\) e. the numbers you roll are not all 5's?

Slot machine A slot machine has three wheels that spin independently. Each has 10 equally likely symbols: 4 bars, 3 lemons, 2 cherries, and a bell. If you play, what is the probability that a. you get 3 lemons? b. you get no fruit symbols? c. you get 3 bells (the jackpot)? d. you get no bells? e. you get at least one bar (an automatic loser)?

Champion bowler A certain bowler can bowl a strike \(70 \%\) of the time. If the bowls are independent, what's the probability that she a. goes three consecutive frames without a strike? b. makes her first strike in the third frame? C. has at least one strike in the first three frames? d. bowls a perfect game (12 consecutive strikes)?

The train To get to work, a commuter must cross train tracks. The time the train arrives varies slightly from day to day, but the commuter estimates he'll get stopped on about \(15 \%\) of work days. During a certain 5 -day work week, what is the probability that he a. gets stopped on Monday and again on Tuesday? b. gets stopped for the first time on Thursday? c. gets stopped every day? d. gets stopped at least once during the week?

Voters Suppose that in your city \(37 \%\) of the voters are registered as Democrats, \(29 \%\) as Republicans, and \(11 \%\) as members of other parties (Liberal, Right to Life, Green, etc.). Voters not aligned with any official party are termed "Independent." You are conducting a poll by calling registered voters at random. In your first three calls, what is the probability you talk to a. all Republicans? b. no Democrats? c. at least one Independent?

Religion Census reports for a city indicate that \(62 \%\) of residents classify themselves as Christian, \(12 \%\) as Jewish, and \(16 \%\) as members of other religions (Muslims, Buddhists, etc.). The remaining residents classify themselves as nonreligious. A polling organization seeking information about public opinions wants to be sure to talk with people holding a variety of religious views, and makes random phone calls. Among the first four people they call, what is the probability they reach a. all Christians? b. no Jews? c. at least one person who is nonreligious?