#made easy test

Question

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

Comments

See Here

https://math.stackexchange.com/questions/537935/a-pair-of-unbiased-dice-are-rolled-together-till-a-sum-of-either-5-or-7-is-obtai

Answer 1

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