IMLOG10ct
2021-11-23
Answered

You roll a die. If it comes up a 6, you win 100. If not, you gettoroll again. If you get a 6 the second time, you win 50. If not, you lose. Find the expected amount you'll win.

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Answered 2021-11-24
Author has **18** answers

Step 1

$$\begin{array}{|cccc|}\hline x& \$0& \$50& \$100\\ P(X=x)& \frac{5}{6}\times \frac{5}{6}=\frac{25}{36}& \frac{5}{6}\times \frac{1}{6}=\frac{5}{36}& \frac{1}{6}\\ \text{Prob. in decimals}& 0.6944& 0.1389& 0.1667\\ \hline\end{array}$$

Step 2

The expected value is the sum of the product of each possibility x with its probability$P(X=x)$ :

$\mu =E\left(X\right)=\sum xP\left(x\right)=0\times \frac{25}{36}+50\times \frac{5}{36}+100\times \frac{1}{6}=\frac{850}{36}\approx \mathrm{\$}23.61}$

Thus the expected amount you will in$\mathrm{\$}23.61}$

Step 2

The expected value is the sum of the product of each possibility x with its probability

Thus the expected amount you will in

Troy Lesure

Answered 2021-11-25
Author has **26** answers

Step 1

We have that "x" is the amount of money earned:

We have to fail twice, the probability of failure is$\frac{5}{6}$ and the probability of hitting is $\frac{1}{6}$ , therefore if you lose the probability would be:

$\frac{5}{6}\times \frac{5}{6}=\frac{25}{36}$

The one to win 50 $, would be:

$\frac{1}{6}\times \frac{5}{6}=\frac{5}{36}$

and the one to win $ 100 would be:

$\frac{1}{6}+\frac{5}{6}=\frac{6}{36}$

that is to say:

$$\begin{array}{|cccc|}\hline x\$& 0\$& 50\$& 100\$\\ p(x)& \frac{25}{36}& \frac{5}{36}& \frac{6}{36}\\ \hline\end{array}$$

We have that "x" is the amount of money earned:

We have to fail twice, the probability of failure is

The one to win 50 $, would be:

and the one to win $ 100 would be:

that is to say:

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