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Problem 1

Three balls are selected at random without replacement from an urn containing four green balls and six red balls. Let the random variable \(X\) denote the number of green balls drawn. a. List the outcomes of the experiment. b. Find the value assigned to each outcome of the experiment by the random variable \(X\). c. Find the event consisting of the outcomes to which a value of 3 has been assigned by \(X\).

Expert verified

a. The possible outcomes are: GGG, GGR, GRG, GRR, RGG, RGR, RRG, RRR.
b. The values assigned by the random variable \(X\):
- GGG: \(X = 3\)
- GGR, GRG, RGG: \(X = 2\)
- GRR, RGR, RRG: \(X = 1\)
- RRR: \(X = 0\)
c. The event with \(X = 3\) is {GGG}.

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Chapter 8

A die is rolled repeatedly until a 6 falls uppermost. Let the random variable \(X\) denote the number of times the die is rolled. What are the values that \(X\) may assume?

Chapter 8

The frequency distribution of the hourly wage rates (in dollars) among blue- collar workers in a certain factory is given in the following table. Find the mean (or average) wage rate, the mode, and the median wage rate of these workers. $$\begin{array}{lcccccc}\hline \text { Wage Rate } & 10.70 & 10.80 & 10.90 & 11.00 & 11.10 & 11.20 \\ \hline \text { Frequency } & 60 & 90 & 75 & 120 & 60 & 45 \\ \hline\end{array}$$

Chapter 8

A survey was conducted by the market research department of the National Real Estate Company among 500 prospective buyers in a large metropolitan area to determine the maximum price a prospective buyer would be willing to pay for a house. From the data collected, the distribution that follows was obtained. Compute the mean, variance, and standard deviation of the maximum price \(x\) (in thousands of dollars) that these buyers were willing to pay for a house. $$ \begin{array}{ll} \hline \text { Maximum Price } & \\ \text { Considered, } x & P(X=x) \\ \hline 280 & \frac{10}{500} \\ \hline 290 & \frac{20}{500} \\ \hline 300 & \frac{75}{500} \\ \hline 310 & \frac{85}{506} \\ \hline 320 & \frac{70}{500} \\ \hline 350 & \frac{90}{500} \\ \hline 380 & \frac{90}{500} \\ \hline 400 & \frac{55}{500} \\ \hline 450 & \frac{5}{500} \\ \hline\end{array}$$

Chapter 8

The management of MultiVision, a cable TV company, intends to submit a bid for the cable television rights in one of two cities, \(A\) or \(B\). If the company obtains the rights to city A, the probability of which is .2, the estimated profit over the next \(10 \mathrm{yr}\) is $$\$ 10$$ million: if the company obtains the rights to city \(\mathrm{B}\), the probability of which is \(.3\), the estimated profit over the next 10 yr is $$\$ 7$$ million. The cost of submitting a bid for rights in city \(\mathrm{A}\) is $$\$ 250,000$$ and that in city B is $$\$ 200,000$$. By comparing the expected profits for each venture, determine whether the company should bid for the rights in city A or city B.

Chapter 8

Let \(X\) denote the random variable that gives the sum of the faces that fall uppermost when two fair dice are rolled. Find \(P(X=7)\).

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