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+1 vote
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asked in Probability by Junior (857 points) | 962 views

2 Answers

+6 votes
Best answer
Favourable cases for 5: {(1,4), (2,3)}
Favourable cases for 7: {(1,6), (2,5), (3,4)}

(I ignored the reverse cases like (4,1) for (1,4) as this happens for both 5 and 7 and hence won't affect the probability)

So, chance that total of 5 comes before 7 = 2/5

(We can ignore all other cases, as questions asks for probability of sum = 5 compared to sum = 7)
answered by Veteran (18k points)
selected by
+5 votes

1/9 is the probability of sum of 5 and 1/6 is the probability of sum of 7. Probability that neither happens = 26/36 = 13/18. 

$$S=1/9 + 13/18  \times 1/9 + \dots $$

In words win5 +loss(5,7)win5 +....

It is a GP series with first term $1/9$ and common ratio $13/18$.

$$ S=\frac{1/9}{(1-(13/18)} =\frac{2}{5}$$

answered by Veteran (14.3k points)
edited by

Your GP series formation is correct way of doing. But the common ratio you got is wrong. You cannot do (8/9) * (5/6) for loss(5,7), as there is only one event happening here. So, probability of loss(5,7) = 1- (10/36) (4 ways of sum becoming 5, and 6 ways of sum becoming 7)
= 13/18 and this would be the ratio of GP.



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