Problem 131
A survey to determine the availability of flextime schedules in the California workplace provided the following information for 220 firms located in two California cities. $$\begin{array}{cccc}\multicolumn{4}{c} {\text { Flextime Schedule }} \\\\\hline \text { City } & \text { Available } & \text { Not Available } & \text { Total } \\\\\hline A & 39 & 75 & 114 \\\B & 25 & 81 & 106 \\\\\hline \text { Totals } & 64 & 156 & 220\end{array}$$ A company is selected at random from this pool of 220 companies. a. What is the probability that the company is located in city \(A\) ? b. What is the probability that the company is located in city \(B\) and offers flextime work schedules? c. What is the probability that the company does not have flextime schedules? d. What is the probability that the company is located in city \(B\), given that the company has flextime schedules available?
Problem 132
An experiment is run as follows- the colors red, yellow, and blue are each flashed on a screen for a short period of time. A subject views the colors and is asked to choose the one he feels was flashed for the longest time. The experiment is repeated three times with the same subject. a. If all the colors were flashed for the same length of time, find the probability distribution for \(x\), the number of times that the subject chose the color red. Assume that his three choices are independent. b. Construct the probability histogram for the random variable \(x\).
Problem 133
A taste-testing experiment is conducted at a local supermarket, where passing shoppers are asked to taste two soft-drink samples - one Pepsi and one Coke \(-\) and state their preference. Suppose that four shoppers are chosen at random and asked to participate in the experiment, and that there is actually no difference in the taste of the two brands. a. What is the probability that all four shoppers choose Pepsi? b. What is the probability that exactly one of the four shoppers chooses Pepsi?
Problem 134
A certain virus afflicted the families in three adjacent houses in a row of 12 houses. If houses were randomly chosen from a row of 12 houses, what is the probability that the three houses would be adjacent? Is there reason to believe that this virus is contagious?
Problem 135
The board of directors of a major symphony orchestra has voted to create a committee for the purpose of handling employee complaints. The committee will consist of the president and vice president of the symphony board and two orchestra representatives. The two orchestra representatives will be randomly selected from a list of six volunteers, consisting of four men and two women. a. Find the probability distribution for \(x\), the number of women chosen to be orchestra representatives. b. What is the probability that both orchestra representatives will be women? able \(x\).
Problem 136
Suppose that \(P(A)=.3\) and \(P(B)=.4\) a. If \(P(A \cap B)=.12\) are \(A\) and \(B\) independent? Justify your answer. b. If \(P(A \cup B)=.7\) what is \(P(A \cap B)\) ? Justify your answer. c. If \(A\) and \(B\) are independent, what is \(P(A \mid B)\) ? d. If \(A\) and \(B\) are mutually exclusive, what is \(P(A \mid B) ?\)
Problem 137
The following information reflects the results of a survey reported by Mya Frazier in an \(A d\) Age Insights white paper. \({ }^{11}\) Working spouses were asked "Who is the household breadwinner?" Suppose that one person is selected at random from these 200 individuals. $$\begin{array}{lcccc} & \multicolumn{3}{c} {\text { Spouse or }} \\\& \text { You } & \text { Significant Other } & \text { About Equal } & \text { Totals } \\\\\hline \text { Men } & 64 & 16 & 20 & 100 \\\\\text { Women } & 32 & 45 & 23 & 100 \\\\\hline \text { Totals } & 96 & 61 & 43 & 200\end{array}$$ a. What is the probability that this person will identify his/herself as the household breadwinner? b. What is the probability that the person selected will be a man who indicates that he and his spouse/significant other are equal breadwinners? c. If the person selected indicates that the spouse or significant other is the breadwinner, what is the probability that the person is a man?
