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


Back to ECE302 Fall 2008 Prof. Sanghavi

Alumni Liaison

Abstract algebra continues the conceptual developments of linear algebra, on an even grander scale.

Dr. Paul Garrett