There is a game with 2 players (A&B) who take turns to roll a die and have to roll a six to win. What is the probability of person A winning?
I got (5/6)^(2n) x (1/6)
Is this correct?
Yup, exactly.. he can win on his first roll, his second roll, his third roll etc..
So, if we let W be the event that a 6 is rolled, and N be the event any other number, and A rolls first, then A will win if the following happens;
W
NNW
NNNNW
NNNNNNW
NNNNNNNNW
etc.
So the probability of these happening;
1/6
etc.
So the Probability of A winning is the sum of the combinations of those events happening
Which is a geometric series