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## Homework Statement

Problem:

Suppose in a certain game a player receives $1 for each "five"

and each "six" thrown on a single die.

a. If the die is thrown six times, find the mean and variance of

the amount the player receives.

b. If the player throws repeatedly until he gets $10, find the

mean of the number of throws necessary

## Homework Equations

## The Attempt at a Solution

Attempt:

I think this is binomial. Then:

1a)

n=6

p=2/6 = 1/3

mean = n*p = 2

variance= n*p*(1-p) = 6*1/3*2/3 = 1/3

Is this correct?

1b)

If $10 is the amount gained,it means:

x=10 (successes)

n=trials

p=1/3

1-p=2/3

=> {n!/[x!(n-x)!]}*(p^10)*(1-p)^(n-10) ???

Is this correct, although tedious?

Thank you very much for any help.