Box 1 has 2 white balls and 2 black balls Box 2 has 2 white balls and 1 black ba

Question

Box 1 has 2 white balls and 2 black balls
Box 2 has 2 white balls and 1 black ball
Box 3 has 1 white ball and 3 black balls

Find probability that the first box was selected given that a ball selected at random is white.

I took the probability that box 1 was selected (1/3) and multiplied it by the probability the ball selected was white given box 1 (1/2) and divided it by the total probability of drawing a white ball (5/11).

I got 11/30 as an answer......is this the correct way to approach this problem? (Bayes Theorem?)

Explanation / Answer

probability that the first box was selected given that a ball selected at random is white =p(white)*p(white of first box) =(2+2+1)/(4+3+4) * (2/(2+2+1))=2/11 [ prob (white)= total white/total=5/11 prob (first box white)=total white in first/total white=2/5] ans =2/11

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