A pair of dice is thrown untill the sum of faces is 5 or 7. Then what is the probability that 5 appears before 7 ?

Probabilty of getting the sum of 5 is P(5) = 4/36 = 1/9 or 2/18
Probabilty of getting the sum of 7 is P(7) = 6/36 = 1/6 or 3/18
So P(5)/P(7) = 2/3 i.e. p(5) will occur 2/3 time as of p(7). so probability of getting 5 before 7 will be 2/(2+3) i.e. 2/5.

Thanks, Vj