There are 1000 players playing a game of dice How many times

There are 1000 players playing a game of dice. How many times must the average player roll before they roll their first 6? Note this problem is not asking the average number of rolls to get a 6, but what the average number of rolls the average player must roll to get their first 6.

Thanks!

Solution

Here p=Prob of getting 6=1/6

X:No. of rolls the average player must roll to get their first 6

X~Geometric(p)

E(X)=1/p=6

Thus,average number of rolls the average player must roll to get their first 6=6