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During the 2014 NFL regular season, kickers converted \(88 \%\) of the field goals attempted. Assume that this percentage is true for all kickers in the upcoming NFL season. Find the probability that a randomly selected kicker who will try 4 field goal attempts in a game will a. convert all 4 field goal attempts b. miss all 4 field goal attempts

A professional basketball player makes \(85 \%\) of the free throws he tries. Assuming this percentage holds true for future attempts, use the binomial formula to find the probability that in the next eight tries, the number of free throws he will make is a. exactly \(8 \quad\) b. exactly 5

Explain the hypergeometric probability distribution. Under what conditions is this probability distribution applied to find the probability of a discrete random variable \(x\) ? Give one example of an application of the hypergeometric probability distribution.

Six jurors are to be selected from a pool of 20 potential candidates to hear a civil case involving a lawsuit between two families. Unknown to the judge or any of the attorneys, 4 of the 20 prospective jurors are potentially prejudiced by being acquainted with one or more of the litigants. They will not disclose this during the jury selection process. If 6 jurors are selected at random from this group of 20 , find the probability that the number of potentially prejudiced jurors among the 6 selected jurors is a. exactly 1 b. none c. at most 2

At the Bank of California, past data show that \(8 \%\) of all credit card holders default at some time in their lives. On one recent day, this bank issued 12 credit cards to new customers. Find the probability that of these 12 customers, eventually a. exactly 3 will default b. exactly 1 will default \(\mathbf{c}\). none will default

Scott offers you the following game: You will roll two fair dice. If the sum of the two numbers obtained is \(2,3,4,9,10,11\), or 12, Scott will pay you \(\$ 20\). However, if the sum of the two numbers is 5 , 6,7, or 8, you will pay Scott \(\$ 20 .\) Scott points out that you have seven winning numbers and only four losing numbers. Is this game fair to you? Should you accept this offer? Support your conclusion with appropriate calculations.

Suppose the owner of a salvage company is considering raising a sunken ship. If successful, the venture will yield a net profit of \(\$ 10\) million. Otherwise, the owner will lose \(\$ 4\) million. Let \(p\) denote the probability of success for this venture. Assume the owner is willing to take the risk to go ahead with this project provided the expected net profit is at least \(\$ 500,000\). a. If \(p=.40\), find the expected net profit. Will the owner be willing to take the risk with this probability of success? b. What is the smallest value of \(p\) for which the owner will take the risk to undertake this project?

Many of you probably played the game "Rock, Paper, Scissors" as a child. Consider the following variation of that game. Instead of two players, suppose three players play this game, and let us call these players \(\mathrm{A}, \mathrm{B}\), and \(\mathrm{C}\). Each player selects one of these three items- Rock, Paper, or Scissors-independent of each other. Player A will win the game if all three players select the same item, for example, rock. Player B will win the game if exactly two of the three players select the same item and the third player selects a different item. Player \(\mathrm{C}\) will win the game if every player selects a different item. If Player B wins the game, he or she will be paid \(\$ 1\). If Player \(\mathrm{C}\) wins the game, he or she will be paid \(\$ 3\). Assuming that the expected winnings should be the same for each player to make this a fair game, how much should Player A be paid if he or she wins the game?