Resolved: "You roll a die. If it comes up..."

IMLOG10ct

Answered question

2021-11-23

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.

Answer & Explanation

Provere

Beginner2021-11-24Added 18 answers

Step 1
$\begin{array}{cc} 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} \\ Prob. in decimals & 0.6944 & 0.1389 & 0.1667 \end{array}$
Step 2
The product of each possibility x and its probability equals the anticipated value. $P (X = x)$ :
$μ = E (X) = \sum x P (x) = 0 \times \frac{25}{36} + 50 \times \frac{5}{36} + 100 \times \frac{1}{6} = \frac{850}{36} \approx $ 23.61$
hence, the anticipated payment you will make $$ 23.61$

Troy Lesure

Beginner2021-11-25Added 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}{cc} x $ & 0 $ & 50 $ & 100 $ \\ p (x) & \frac{25}{36} & \frac{5}{36} & \frac{6}{36} \end{array}

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