91Ó°ÊÓ

Given that \(A\) and \(B\) are two independent events, find their joint probability for the following. a. \(P(A)=.61\) and \(P(B)=.27\) b. \(P(A)=.39\) and \(P(B)=.63\)

Given that \(P(A)=.30\) and \(P(A\) and \(B)=.24\), find \(P(B \mid A)\).

The following table gives a two-way classification of all basketball players at a state university who began their college careers between 2001 and 2005, based on gender and whether or not they graduated \(\begin{array}{lcc} \hline & \text { Graduated } & \text { Did Not Graduate } \\ \hline \text { Male } & 126 & 55 \\ \text { Female } & 133 & 32 \\ \hline \end{array}\) a. If one of these players is selected at random, find the following probabilities. i. \(P(\) female and graduated \()\) ii. \(P(\) male and did not graduate \()\) b. Find \(P\) (graduated and did not graduate). Is this probability zero? If yes, why?

Two thousand randomly selected adults were asked if they think they are financially better off than their parents. The following table gives the two- way classification of the responses based on the education levels of the persons included in the survey and whether they are financially better off, the same as. or worse off than their parents. $$\begin{array}{lccc} \hline & \begin{array}{c} \text { Less Than } \\ \text { High School } \end{array} & \begin{array}{c} \text { High } \\ \text { School } \end{array} & \begin{array}{c} \text { More Than } \\ \text { High School } \end{array} \\ \hline \text { Better off } & 140 & 450 & 420 \\ \text { Same as } & 60 & 250 & 110 \\ \text { Worse off } & 200 & 300 & 70 \\ \hline \end{array}$$ a. Suppose one adult is selected at random from these 2000 adults. Find the following probabilities. i. \(P\) (better off and high school) ii. \(P(\) more than high school and worse off ) b. Find the joint probability of the events "worse off" and "better off." Is this probability zero? Explain why or why not.

In a statistics class of 42 students, 28 have volunteered for community service in the past. If two students are selected at random from this class, what is the probability that both of them have volunteered for community service in the past? Draw a tree diagram for this problem.

Suppose that \(20 \%\) of all adults in a small town live alone, and \(8 \%\) of the adults live alone and have at least one pet. What is the probability that a randomly selected adult from this town has at least one pet given that this adult lives alone?

When is the following addition rule used to find the probability of the union of two events \(A\) and \(B\) ? $$P(A \text { or } B)=P(A)+P(B)$$ Give one example where you might use this formula.

Given that \(A\) and \(B\) are two mutually exclusive events, find \(P(A\) or \(B\) ) for the following. a. \(P(A)=.25\) and \(P(B)=.27\) b. \(P(A)=.58\) and \(P(B)=.09\)

In a sample survey, 1800 senior citizens were asked whether or not they have ever been victimized by a dishonest telemarketer. The following table gives the responses by age group. $$\begin{array}{l|llcc} & & & \begin{array}{c} \text { Have Been } \\ \text { Victimized } \end{array} & \begin{array}{c} \text { Have Never } \\ \text { Been Victimized } \end{array} \\ \hline & 60-69 & \text { (A) } & 106 & 698 \\ \text { Age } & 70-79 & \text { (B) } & 145 & 447 \\ & 80 \text { or over (C) } & 61 & 343 \\ \hline \end{array}$$ Suppose one person is randomly selected from these senior citizens. Find the following probabilities a. \(P(\) have been victimized or \(\mathrm{B}\) ) b. \(P(\) have never been victimized or \(\mathrm{C}\) )

According to a survey of 2000 home owners, 800 of them own homes with three bedrooms, and 600 of them own homes with four bedrooms. If one home owner is selected at random from these 2000 home owners, find the probability that this home owner owns a house that has three or four bedrooms. Explain why this probability is not equal to \(1.0 .\)