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Chapter 4: Problem 72
Given that \(P(A \mid B)=.44\) and \(P(A\) and \(B)=.33\), find \(P(B)\).
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Determine the value of each of the following using the appropriate formula. $$ \begin{array}{llllllllll} 3 ! & (9-3) ! & 9 ! & (14-12) ! & { }_{5} C_{3} & { }_{7} C_{4} & { }_{9} C_{3} & { }_{4} C_{0} & { }_{3} C_{3} & { }_{6} P_{2} & { }_{8} P_{4} \end{array} $$
The probability that a farmer is in debt is 80 . What is the probability that three randomly selected farmers are all in debt? Assume independence of events.
A thief has stolen Roger's automatic teller machine (ATM) card. The card has a four-digit personal identification number (PIN). The thief knows that the first two digits are 3 and 5 , but he does not know the last two digits. Thus, the PIN could be any number from 3500 to \(3599 .\) To protect the customer, the automatic teller machine will not allow more than three unsuccessful attempts to enter the PIN. After the third wrong PIN, the machine keeps the card and allows no further attempts. a. What is the probability that the thief will find the correct PIN within three tries? (Assume that the thief will not try the same wrong PIN twice.) b. If the thief knew that the first two digits were 3 and 5 and that the third digit was either 1 or 7 , what is the probability of the thief guessing the correct PIN in three attempts?
Powerball is a game of chance that has generated intense interest because of its large jackpots. To play this game, a player selects five different numbers from 1 through 59, and then picks a Powerball number from 1 through \(39 .\) The lottery organization randomly draws 5 different white balls from 59 balls numbered 1 through 59 , and then randomly picks a Powerball number from 1 through \(39 .\) Note that it is possible for the Powerball number to be the same as one of the first five numbers. a. If a player's first five numbers match the numbers on the five white balls drawn by the lottery organization and the player's Powerball number matches the Powerball number drawn by the lottery organization, the player wins the jackpot. Find the probability that a player who buys one ticket will win the jackpot. (Note that the order in which the five white balls are drawn is unimportant.) b. If a player's first five numbers match the numbers on the five white balls drawn by the lottery organization, the player wins about \(\$ 200,000\). Find the probability that a player who buys one ticket will win this prize.
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?
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