Probability of obtaining 7 before 8 with pair of fair dice

[squaremeplz]

Homework Statement

A pair of fair dice is rolled until the first 8 appears. What is the probability that a sum of 7 does not precede a sum of 8.

Homework Equations

Geometric series

The Attempt at a Solution

P(sum of 7 does not appear before sum of 8) =

5/36 + 5/36 * 25/36 + 5/36 *(25/36)^2 + ...

= (5/36)/(1-25/36) = 5/11

do I have to use geometric series for this or just find the prob of 7 before 8?

Thanks!

 

[Dick]

Yes, I think you need to use a geometric series. Either 7 or 8 appearing ends the game, right? So I think you need to find the probability that neither 7 nor 8 appears in k-1 rolls times the probability that 8 appears on the kth roll. Then sum over all k.

 

[Dick]

Homework Statement

A pair of fair dice is rolled until the first 8 appears. What is the probability that a sum of 7 does not precede a sum of 8.

Homework Equations

Geometric series

The Attempt at a Solution

P(sum of 7 does not appear before sum of 8) =

5/36 + 5/36 * 25/36 + 5/36 *(25/36)^2 + ...

= (5/36)/(1-25/36) = 5/11

do I have to use geometric series for this or just find the prob of 7 before 8?

Thanks!

I think that's correct 5/36 is the probability of 8 and 25/36 is the probability of neither 7 nor 8. You did do a geometric series. How can you compute the probability of 7 before 8 without it?

 

[squaremeplz]

I don't think it is possible without using a geometric series because it's a problem of infinite sum.