The Dice Game, GCSE coursework helpWatch
My teacher added various questions which he said we should include to complete the coursework, one of which I'm having trouble with:
Investigate the probability of A, B or C winning on subsequent goes.
For A, the probability of winning is 1/6 on his first go, then, because he wins with rolling a 1, the game starts again, starting with A rolling, his probability of winning is again 1/6 therefore winning on subsequent goes is 1/6*1/6 = 1/36. However I've been told that the answer is 5/108. Could someone tell me how that answer could be obtained?
So, B and C have to roll before A gets their next go.
Doesn't A winning on subsequent goes mean A wins 2 times in a row? I thought that on the first go, A rolls a 1 and wins the game. The game then starts again with A because B doesn't have a go so when A rolls once more and wins the overall probability is 1/36. I've spent hours trying to work out alternate ways. Any hints to how I'm supposed to do this?
Probability A wins second go means
A lost, B lost, C lost, A won.
I agree 1/36 is the prob of A winning 2 games in a row.