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Experiment: Box 0 contains 2 colored balls and one white ball | Experiment: Box 0 contains 2 colored balls and one white ball | ||
Box 1 contains 1 color ball and 2 white balls | Box 1 contains 1 color ball and 2 white balls | ||
Given the color of the ball pick which box it came from. | Given the color of the ball pick which box it came from. | ||
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X = color or white ball | X = color or white ball | ||
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If x = white then pick Box 1 | If x = white then pick Box 1 | ||
If x = color then pick either box | If x = color then pick either box | ||
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| + | [[Main_Page_ECE302Fall2008sanghavi|Back to ECE302 Fall 2008 Prof. Sanghavi]] | ||
Latest revision as of 13:44, 22 November 2011
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
