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Chapter 4: Problem 84
How many different outcomes are possible for 10 tosses of a coin?
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The probability that an open-heart operation is successful is \(.84\). What is the probability that in two randomly selected open-heart operations at least one will be successful?
The president of a company has a hunch that there is a \(.80\) probability that the company will be successful in marketing a new brand of ice cream. Is this a case of classical, relative frequency, or subjective probability? Explain why.
The probability that a student graduating from Suburban State University has student loans to pay off after graduation is .60. If two students are randomly selected from this university, what is the probability that neither of them has student loans to pay off after graduation?
A player plays a roulette game in a casino by betting on a single number each time. Because the wheel has 38 numbers, the probability that the player will win in a single play is \(1 / 38\). Note that each play of the game is independent of all previous plays. a. Find the probability that the player will win for the first time on the 10 th play. b. Find the probability that it takes the player more than 50 plays to win for the first time. c. A gambler claims that because he has 1 chance in 38 of winning each time he plays, he is certain to win at least once if he plays 38 times. Does this sound reasonable to you? Find the probability that he will win at least once in 38 plays.
Consider the following games with two dice. a. A gambler is going to roll a die four times. If he rolls at least one 6 , you must pay him \(\$ 5\). If he fails to roll a 6 in four tries, he will pay you \(\$ 5\). Find the probability that you must pay the gambler. Assume that there is no cheating. b. The same gambler offers to let you roll a pair of dice 24 times. If you roll at least one double 6 , he will pay you \(\$ 10\). If you fail to roll a double 6 in 24 tries, you will pay him \(\$ 10\). The gambler says that you have a better chance of winning because your probability of success on each of the 24 rolls is \(1 / 36\) and you have 24 chances. Thus, he says, your probability of winning \(\$ 10\) is \(24(1 / 36)=2 / 3\). Do you agree with this analysis? If so, indicate why. If not, point out the fallacy in his argument, and then find the correct probability that you will win.
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