91Ó°ÊÓ

In seven-card stud poker, a player is dealt seven cards. The probability that the player is dealt two cards of the same value and five other cards of different value so that the player has a pair is \(0.44 .\) Explain what this probability means. If you play seven-card stud 100 times, will you be dealt a pair exactly 44 times? Why or why not?

According to the U.S. Census Bureau, \(8.0 \%\) of 16 - to 24 -year-olds are high school dropouts. In addition, \(2.1 \%\) of 16 - to 24 -year-olds are high school dropouts and unemployed. What is the probability that a randomly selected 16 - to 24 -year-old is unemployed, given he or she is a dropout?

False Positives The ELISA is a test to determine whether the HIV antibody is present. The test is \(99.5 \%\) effective, which means that the test will come back negative if the HIV antibody is not present \(99.5 \%\) of the time. The probability of a test coming back positive when the antibody is not present (a false positive) is \(0.005 .\) Suppose that the ELISA is given to five randomly selected people who do not have the HIV antibody. (a) What is the probability that the ELISA comes back negative for all five people? (b) What is the probability that the ELISA comes back positive for at least one of the five people?

List all combinations of five objects \(a, b, c, d,\) and \(e\) taken three at a time without replacement.

Christmas lights are often designed with a series circuit. This means that when one light burns out the entire string of lights goes black. Suppose that the lights are designed so that the probability a bulb will last 2 years is \(0.995 .\) The success or failure of a bulb is independent of the success or failure of other bulbs. (a) What is the probability that in a string of 100 lights all 100 will last 2 years? (b) What is the probability that at least one bulb will burn out in 2 years?

In a recent Harris Poll, a random sample of adult Americans (18 years and older) was asked, "When you see an ad emphasizing that a product is 'Made in America,' are you more likely to buy it, less likely to buy it, or neither more nor less likely to buy it?" The results of the survey, by age group, are presented in the following contingency table. $$ \begin{array}{lrrrrr} & \mathbf{1 8 - 3 4} & \mathbf{3 5 - 4 4} & \mathbf{4 5 - 5 4} & \mathbf{5 5 +} & \text { Total } \\ \hline \text { More likely } & 238 & 329 & 360 & 402 & \mathbf{1 3 2 9} \\ \hline \text { Less likely } & 22 & 6 & 22 & 16 & \mathbf{6 6} \\ \hline \begin{array}{l} \text { Neither more } \\ \text { nor less likely } \end{array} & 282 & 201 & 164 & 118 & \mathbf{7 6 5} \\ \hline \text { Total } & \mathbf{5 4 2} & \mathbf{5 3 6} & \mathbf{5 4 6} & \mathbf{5 3 6} & \mathbf{2 1 6 0} \end{array} $$ (a) What is the probability that a randomly selected individual is 35-44 years of age, given the individual is more likely to buy a product emphasized as "Made in America"? (b) What is the probability that a randomly selected individual is more likely to buy a product emphasized as "Made in America," given the individual is \(35-44\) years of age? (c) Are 18 - to 34 -year-olds more likely to buy a product emphasized as "Made in America" than individuals in general?

In a survey of 500 randomly selected Americans, it was determined that 22 play soccer. What is the probability that a randomly selected American plays soccer?

In Problems 13-18, find the probability of the indicated event if \(P(E)=0.25\) and \(P(F)=0.45\) \(P\left(F^{c}\right)\)

Adult Americans (18 years or older) were asked whether they used social media (Facebook, Twitter, and so on ) regularly. The following table is based on the results of the survey. $$ \begin{array}{lccccc} & \mathbf{1 8 - 3 4} & \mathbf{3 5 - 4 4} & \mathbf{4 5 - 5 4} & \mathbf{5 5 +} & \text { Total } \\ \hline \begin{array}{l} \text { Use social } \\ \text { media } \end{array} & 117 & 89 & 83 & 49 & \mathbf{3 3 8} \\ \hline \begin{array}{l} \text { Do not use } \\ \text { social media } \end{array} & 33 & 36 & 57 & 66 & \mathbf{1 9 2} \\ \hline \text { Total } & \mathbf{1 5 0} & \mathbf{1 2 5} & \mathbf{1 4 0} & \mathbf{1 1 5} & \mathbf{5 3 0} \\ \hline \end{array} $$ (a) What is the probability that a randomly selected adult American uses social media, given the individual is \(18-34\) years of age? (b) What is the probability that a randomly selected adult American is \(18-34\) years of age, given the individual uses social media? (c) Are 18 - to 34 -year olds more likely to use social media than individuals in general? Why?

Find the value of each permutation. $$ { }_{9} P_{4} $$