elmarsur
Nov2-09, 03:14 PM
1. The problem statement, all variables and given/known data
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
2. Relevant equations
3. 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.
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
2. Relevant equations
3. 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.