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Chapter 5: Q 42. (page 309)
Tossing coins Refer to Exercise 40. Define event : get more heads than tails. Find .
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The casino game craps is based on rolling two dice. Here is the assignment of probabilities to the sum of the numbers on the up-faces when two dice are rolled: pass line bettor wins immediately if either a or an comes up on the first roll. This is called a natural. What is the probability of a natural?
(a) (c) (e)
(b) (d)
Going pro Only of male high school basketball, baseball, and football players go on to play at the college level. Of these, only enter major league professional sports. About of the athletes who compete in college and then reach the pros have a career of more than years. What is the probability that a high school athlete who plays basketball, baseball, or football competes in college and then goes on to have a pro career of more than years? Show your work.
Languages in Canada Canada has two official languages, English and French. Choose a Canadian at random and ask, 鈥淲hat is your mother tongue?鈥�
Here is the distribution of responses, combining many separate languages from the broad Asia/Pacific region:Language: English French Asian/Pacific Other Probability: ?
(a) What probability should replace 鈥�?鈥� in the distribution? Why?
(b) What is the probability that a Canadian鈥檚 mother tongue is not English?
(c) What is the probability that a Canadian鈥檚 mother tongue is a language other than English or French?
Liar, liar! Sometimes police use a lie detector (also known as a polygraph) to help determine whether a suspect is telling the truth. A lie detector test isn鈥檛 foolproof鈥攕ometimes it suggests that a person is lying when they鈥檙e actually telling the truth (a 鈥渇alse positive鈥�). Other times, the test says that the suspect is being truthful when the person is actually lying (a 鈥渇alse negative鈥�). For one brand of polygraph machine, the probability of a false positive is .
(a) Interpret this probability as a long-run relative frequency.
(b) Which is a more serious error in this case: a false positive or a false negative? Justify your answer.
Taking the train According to New Jersey Transit, the 8:00 a.m. weekday train from Princeton to New York City has a 90% chance of arriving on time. To test this claim, an auditor chooses 6 weekdays at random during a month to ride this train. The train arrives late on 2 of those days. Does the auditor have convincing evidence that the company鈥檚 claim isn鈥檛 true? Design and carry out a simulation to answer this question. Follow the four-step process.
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