Probability of obtaining 7 before 8 with pair of fair dice

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Homework Help Overview

The problem involves rolling a pair of fair dice until the first occurrence of a sum of 8, with the goal of determining the probability that a sum of 7 does not occur before the sum of 8. The context is rooted in probability theory and geometric series.

Discussion Character

  • Exploratory, Mathematical reasoning

Approaches and Questions Raised

  • Participants discuss the use of geometric series to calculate the probability, with some suggesting that the game ends when either a 7 or an 8 appears. Questions arise about whether a geometric series is necessary or if there are alternative methods to find the probability of rolling a 7 before an 8.

Discussion Status

The discussion is ongoing, with participants exploring the necessity of geometric series in solving the problem. Some express confidence in the approach taken, while others emphasize the infinite nature of the sums involved.

Contextual Notes

There is a focus on the probabilities associated with rolling sums of 7 and 8, and the implications of these probabilities on the overall problem setup. The discussion reflects uncertainty about the best method to approach the calculation.

squaremeplz
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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!
 
Last edited:
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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.
 


squaremeplease said:

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?
 
Last edited:


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

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