Question

Experiment: Box 0 contains 2 colored balls and one white ball

           Box 1 contains 1 color ball and 2 white balls

Given the color of the ball pick which box it came from.

Answer

X = color or white ball

Pr[B0] = 1/3 Pr[B1] = 2/3

Pr[white|B0] = 1/3 Pr[white|B1] = 2/3 Pr[color|B0] = 2/3 Pr[color|B2] = 1/3

MAP Rule: Pick the Box i (i = 0,1) with largest Pr[x|Bi]*Pr[Bi]

if x = white Pr[white|B0]*P[B0] = (1/3)*(1/3) = 1/9

              Pr[white|B1]*P[B1] = (2/3)*(2/3) = 4/9

if x = color Pr[color|B0]*P[B0] = (2/3)*(1/3) = 2/9

              Pr[color|B1]*P[B1] = (1/3)*(2/3) = 2/9

If x = white then pick Box 1 If x = color then pick either box