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Question

A bag contains 4 balls. Two balls are drawn at random and are found to be white. what is the probability that all the balls in the bag are white?

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Solution

E1:2 balls are white, 2 are non white
E2:3 balls are white, 1 is not white
E3:4 balls are white
A: Two balls are white
P(E1)=13,P(E2)=13,P(E3)=13
P(A|E1)=2C24C2=16
P(A|E2)=3C24C2=36=12,P(A|E3)=4C24C2=1
P(E3|A)=P(A|E3)P(E3)P(A|E1)P(E1)+P(A|E2)P(E2)+P(A|E3)P(E3)
=1×1316×13+12×13+13×1=116+12+1=610=35

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