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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

45. Too cool at the cabin? During the winter months, the temperatures at the Stameses' Colorado cabin can stay well below freezing 32掳For 0掳Cfor weeks at a time. To prevent the pipes from freezing, Mrs. Stames sets the thermostat at 50掳F. She also buys a digital thermometer that records the indoor temperature each night at midnight. Unfortunately, the thermometer is programmed to measure the temperature in degrees Celsius. Based on several years' worth of data, the temperature Tin the cabin at midnight on a randomly selected night follows a Normal distribution with mean 8.5掳Cand standard deviation2.25掳C.
(a) Let Y=the temperature in the cabin at midnight on a randomly selected night in degrees Fahrenheit (recall that F=(9/5)C+32). Find the mean and standard deviation of Y.

(b) Find the probability that the midnight temperature in the cabin is below 40掳F. Show your work.

77. Blood types Refer to Exercise 75. How surprising would it be to get more than 4 adults with type O blood in the sample? Calculate an appropriate probability to support your answer.

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鈥檚 grade on the quiz (out of 100), Ms. Hall will multiply his or her number of correct answers by 10. Let G=the grade of a randomly chosen student in the class.

NMeanMedianStDevMinMaxQ1Q3307.68.51.3241089

(a) Find the median of G. Show your method.

(b) Find the IQR of G. Show your method.

(c) What shape would the probability distribution of Ghave? Justify your answer

25. Did you vote? A sample survey contacted an SRS of 663 registered voters in Oregon shortly after an election and asked respondents whether they had voted. Voter records show that 56%of registered voters had actually voted. We will see later that in repeated random samples of size 663, the proportion in the sample who voted (call this proportion V) will vary according to the Normal distribution with mean 渭=0.56 and standard deviation 蟽=0.019.
(a) If the respondents answer truthfully, what is P(0.52鈮�V鈮�0.60)? This is the probability that the sample proportion V estimates the population
proportion 0.56 within 卤0.04.
(b) In fact, 72%of the respondents said they had voted (V=0.72). If respondents answer truthfully, what is P(V鈮�0.72)? This probability is so small that it is good evidence that some people who did not vote claimed that they did vote.

In a process for manufacturing glassware, glass stems are sealed by heating them in a flame. The temperature of the flame can be adjusted to one of five different settings. Here is the probability distribution of the flame temperature X(in degrees Celsius) for a randomly chosen glass:

渭X=550掳C蟽X=5.7掳C

(a) The target temperature is550掳C. What are the mean and standard deviation of the number of degrees off target, D=X鈭�550?

(b) A manager asks for results in degrees Fahrenheit. The conversion of X into degrees Fahrenheit is given by \(y=\frac{9}{5} X+32\). What are the mean 渭Y and the standard deviation 蟽Y of the temperature of the flame in the Fahrenheit scale?
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