# Die throwing probability question

## 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

## 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.