Four dice are in a box 1 die is weighted so a two appears on

Four dice are in a box. 1 die is weighted so a two appears on 1/5 of all rolls. The remaining 3 dice are fair. A child picks a die at random and rolls a two. What is the probability that the die picked was fair? Show all work so I know how to do future problems.

Solution

Four dice are in a box. 1 die is weighted so a two appears on 1/5 of all rolls. The remaining 3 dice are fair. A child picks a die at random and rolls a two. What is the probability that the die picked was fair?

ans-

let A event is die was fair and B event is 2 appears

P(A / B)=  P(A intersection B)/ P(B)

P(A intersection B)= (1/3)*(1/5) = 1/15

P(B)= (1/3)*(1/5) + (2/3)*(1/6) =8/45

P(A / B)= (1/15)/(8/45)= 3/8