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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

Kids and toys Refer to Exercise 4. Calculate and interpret the standard deviation of the random variable X. Show your work.

Ana is a dedicated Skee Ballplayer (see photo) who always rolls for the 50-point slot. The probability distribution of Ana's score Xon a single roll of the ball is shown below. You can check that 渭X=23.8and 蟽X=12.63.

(a) A player receives one ticket from the game for every 10points scored. Make a graph of the probability distribution for the random variable T=number of tickets Ana gets on a randomly selected throw. Describe its shape.

(b) Find and interpret 渭T.

(c) Compute and interpret 蟽T.

A large auto dealership keeps track of sales made during each hour of the day. Let X= the number of cars sold during the 铿乺st hour of business on a randomly selected Friday. Based on previous records, the probability distribution of Xis as follows:

The random variable Xhas mean 渭X=1.1and standard deviation 蟽X=0.943.

Suppose the dealership鈥檚 manager receives a 500bonus from the company for each car sold. Let Y = the bonus received from car sales during the 铿乺st hour on a randomly selected Friday. Find the mean and standard deviation of Y.

14. . Life insurance A life insurance company sells a term insurance policy to a 21-year-old male that pays \(100,000if the insured dies within the next 5years. The probability that a randomly chosen male will die each year can be found in mortality tables. The company collects a premium of \)250each year a payment for the insurance. The amount Ythat the company earns on this policy is \(250per year, less the \)100,000that it must pay if the insured dies. Here is a partially completed table that shows information about risk of mortality and the values of Y=profit earned by the company:

(a) Copy the table onto your paper. Fill in the missing values of Y.
(b) Find the missing probability. Show your work.
(c) Calculate the mean 渭Y.Interpret this value in context

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

Find P(T=3). Interpret this result in context.
See all solutions

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