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Chapter 4: Problem 29
In a group of 50 car owners, 8 own hybrid cars. If one car owner is selected at random from this group, what is the probability that this car owner owns a hybrid car?
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A certain state's auto license plates have three letters of the alphabet followed by a three-digit number. a. How many different license plates are possible if all three-letter sequences are permitted and any number from 000 to 999 is allowed? b. Arnold witnessed a hit-and-run accident. He knows that the first letter on the license plate of the offender's car was a \(\mathrm{B}\), that the second letter was an \(\mathrm{O}\) or a \(\mathrm{Q}\), and that the last number was a 5. How many of this state's license plates fit this description?
A restaurant menu has four kinds of soups, eight kinds of main courses, five kinds of desserts, and six kinds of drinks. If a customer randomly selects one item from each of these four categories, how many different outcomes are possible?
According to the May 2009 issue of \(U . S\). News and World Report, \(85.1 \%\) of the students who graduated with an MBA degree in 2008 from the University of Virginia's Darden School of Business had job offers before the graduation date. Suppose that this percentage is true for the top \(50 \mathrm{MBA}\) programs in the list of 426 MBA programs analyzed in this issue of the U.S. News and World Report. Suppose that two 2008 MBA graduates are selected at random from these top 50 MBA programs and asked if they had job offers before the graduation date. Draw a tree diagram for this problem. Find the probability that in this sample of two graduates a. both had job offers before the graduation date b. at most one had job offer before the graduation date
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. If one adult is selected at random from these 2000 adults, find the probability that this adult is i. financially better off than his/her parents ii. financially better off than his/her parents given he/she has less than high school education iii. financially worse off than his/her parents given he/she has high school education jy. financially the same as his/her parents given he/she has more than high school education b. Are the events "better off" and "high school" mutually exclusive? What about the events "less than high school" and "more than high school?" Why or why not? c. Are the events "worse off" and "more than high school" independent? Why or why not?
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?
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