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A pair of dice rolled together till a sum of either 5 or 7 obtained. find probability that 5 comes before 7.

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Probability of getting a sum of 5 = P(A)=4/36=1/9

Probability of getting a sum of 7 = P(B)=6/36=1/6

Probability that neither happens = P(N)=(1-10/36)=26/36

P(A happens before B) = P(A) + neither happen then A happens i.e.P(N)P(A)+ neither happens then neither happen then A happens i.e.P(N)P(N)P(A) + so on

It is an infinite Geometric Progression.

p =(1/9)/(1−(13/18))

p = 2/5

Probability of getting a sum of 7 = P(B)=6/36=1/6

Probability that neither happens = P(N)=(1-10/36)=26/36

P(A happens before B) = P(A) + neither happen then A happens i.e.P(N)P(A)+ neither happens then neither happen then A happens i.e.P(N)P(N)P(A) + so on

It is an infinite Geometric Progression.

p =(1/9)/(1−(13/18))

p = 2/5

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