The Dice Game, GCSE coursework help

I've been having a lot of trouble with my maths coursework on a dice game, the site below gives a link to download the question sheet for microsoft word:

http://www.warwick.surrey.sch.uk/student%20zone/Maths/gcse_coursework1_tasks.htm

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?

Reply 1

gilyan

Are you sure it's the right answer? Have you drawn a tree diagram?

Reply 2

gilyan

Right, I've read the file now and I agree with the 5/108. So, your question is what is the prob of A winning on their second go - you need to draw the tree diagram - and remember that if A doesn't have 2 throws, B has the second go.

So, B and C have to roll before A gets their next go.

Reply 3

Kanes_mask

I think I maybe confused with the questioning,

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?

Reply 4

gilyan

Assuming subsequent goes means same game - not new game, I'd check with you teacher.

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.

Reply 5

Kanes_mask

Thankyou, you've saved me from hours more work, I can't believe it was that simple, I was confused by the term 'subsequent'. Unfortunately I've already done a considerable amount of work with the asumption that A winning on subsequent goes is 1/36. I've just jotted a few notes using the information you've given and have come up with the formula 1/6(5/18)^n-1 which solves a lot of the problems I've been having. Thanks once again.