Stats help please!!!!!!

Original post by MikeySwansea

Hi all,

Got a question on probability for you, would really appreciate someone explaining it to me, here goes:

Two children, Ann and Brian, throw a die alternately and the first to throw a '6' is the winner. Given that Ann throws first, calculate the probability that Brian wins

(A) on his nth throw

Use (A) to calculate the probability that Brian wins the game

I have the answer to (A), it is 1/6(5/6)^ 2n-1 and understand how I have come to the answer, I am also able to get an answer like this for Ann.

I just can't seem to work out how to calculate the probability that Brian wins using my answer to (A)

Thanks in advance

Consider all the possibily ways that Brian could win, and add up their probabilities.

Reply 2

OP

Thanks for the reply, I'm afraid I just can't see it.

Can you explain it to me more please, sorry to be a pain

Reply 3

Original post by MikeySwansea

Thanks for the reply, I'm afraid I just can't see it.

Can you explain it to me more please, sorry to be a pain

P(Brian wins) = P(Brian wins on first go) + P(Brian wins on second go) + ....

Hint:

Spoiler

(edited 12 years ago)

Reply 4

OP

Hi Ghostwalker, I understand that part of it, but I'm struggling to see where it ends, I mean for e.g it could take a thousand turns.

Reply 5

Classical Liberal

19

Original post by MikeySwansea

Hi all,

Got a question on probability for you, would really appreciate someone explaining it to me, here goes:

Two children, Ann and Brian, throw a die alternately and the first to throw a '6' is the winner. Given that Ann throws first, calculate the probability that Brian wins

(A) on his nth throw

Use (A) to calculate the probability that Brian wins the game

I have the answer to (A), it is 1/6(5/6)^ 2n-1 and understand how I have come to the answer, I am also able to get an answer like this for Ann.

I just can't seem to work out how to calculate the probability that Brian wins using my answer to (A)

Thanks in advance

What is the chance that A will roll a 6 on the first go?

1/6

Second go? (fail first, then B fails)

5/6 * 5/6 * 1/6

Third go? (fail first, then B fails, then fail again, then B fails)

5/6 * 5/6 * 5/6 * 5/6 * 1/6

Can you see a pattern developing?

btw if you start at n=1 then I think the exponent should be 2n-2 not 2n-1

(edited 12 years ago)

Reply 6

Original post by MikeySwansea

Hi Ghostwalker, I understand that part of it, but I'm struggling to see where it ends, I mean for e.g it could take a thousand turns.

There is no end; it's an infinite series, whose terms follow a geometric progression.

(edited 12 years ago)

Reply 7

OP

Cant see any pattern, the answer is 5/11 and I don't have a clue how to get there

Reply 8

TenOfThem

18

you already have the terms for Brian winning

\frac{1}{6}(\frac{5}{6})^{2n-1}

The general term in a GP is

ar^{n-1}

And you presumably know the sum to infinity of a GP

All that you need to do is compare your term with the general term

Reply 9

OP

Hi all,

I really don't know how to do this question, I haven't been taught about the Geometric Progression yet in class. Having looked at a few websites I'm still confused on how to apply the formula to this question in order to get the probability of him winning.

Please would someone be able to spell it out for me, I'd be extremely grateful.

Reply 10