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Chapter 6: Q.4.3 (page 401)

Suppose you roll a pair of fair, six-sided dice until you get doubles. Let T=the number of rolls it takes.

In the game of Monopoly, a player can get out of jail free by rolling doubles within 3turns. Find the probability that this happens

Short Answer

Expert verified

The probability is0.4213.

Step by step solution

01

Given Information

Given that there are two pairs of dice that are being rolled to get doubles.

The variable T shows the number of rolls dice take.

02

Calculation

The pdf of geometric distribution is:

P(X=k)=(1-p)k-1p

The probability of success 16.

The probability using Ti-83plus calculator can be calculated as

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Most popular questions from this chapter

Ms. Hall gave her class a 10-question multiple-choice quiz. Let X=the number of questions that a randomly selected student in the class answered correctly. The computer output below gives information about the probability distribution of X. To determine each student’s grade on the quiz (out of localid="1649489099543" 100), Ms. Hall will multiply his or her number of correct answers by 10. Let localid="1649489106434" G=the grade of a randomly chosen student in the class.

localid="1649489113566" NMeanMedianStDevMinMaxQ1Q3307.68.51.3241089

(a) Find the mean of localid="1649489121120" G. Show your method.

(b) Find the standard deviation of localid="1649489127059" G. Show your method.

(c) How do the variance of localid="1649489132289" Xand the variance oflocalid="1649489138146" Gcompare? Justify your answer.

A housing company builds houses with two-car garages. What percent of households have more cars than the garage can hold? (a) 13%

(b) 20%

(c) 45%

(d) 55%

(e) 80%

Binomial setting? A binomial distribution will be approximately correct as a model for one of these two settings and not for the other. Explain why by briefly discussing both settings. (a) When an opinion poll calls residential telephone numbers at random, only 20%of the calls reach a person. You watch the random digit dialing machine make 15calls. Xis the number that reaches a person

(b) When an opinion poll calls residential telephone numbers at random, only 20%of the calls reach a live person. You watch the random digit dialing machine make calls. Yis the number of calls until the first live person answers

Explain whether the given random variable has a binomial distribution.

Lefties Exactly 10%of the students in a school are left-handed. Select students at random from the school, one at a time, until you find one who is left-handed. Let V=the number of students chosen.

Running a mile A study of 12,000able-bodied male students at the University of Illinois found that their times for the mile run were approximately Normal with mean 7.11minutes and standard deviation 0.74 minute. Choose a student at random from this group and call his time for the mile Y. Find P(Y<6) and interpret the result. Follow the four-step process.
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