What is the Conditional Probability of Selecting Box B Given a White Ball?

[naspek]

box A contains 2 red balls,
box B contains 2 white balls,
box C contains 1 red ball and 1 white ball,

A box is selected at random (with equal probabilities) and one ball is taken at random from that box.

(i) Compute the probability of selecting a white ball using Bayes Rule.

A(1/3) _____ Red(1/6)
...|____ Red(1/6)

B(1/3)______White(1/6)
...|_____White(1/6)

C(1/3)______Red(1/6)
...|_____White(1/6)

so.. P(White) = [(1/3)*(1/6)] + [(1/3)*(1/6)] + [(1/3)*(1/6)]
= 1/6

Correct?

(ii)Compute the conditional probability that B has been selected given that the ball is white.

P(B|White) = P(B intersect White) / P(White)

what is my P(B intersect White)?

 

[kurt.physics]

P(B intersect White) = P(B) * P(White|B) = (1/3) * (1/6) = 1/18Therefore, P(B|White) = P(B intersect White)/P(White) = (1/18)/(1/6) = 1/3