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A jar has m red balls and n black balls. we draw two balls from the .pdf

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A jar contains m red balls and n black balls. The document defines probabilities for drawing balls from the jar: a) The probability the first ball drawn is red is m/(m+n). b) The probability the second ball is black given the first was red is [m/(m+n)]*[n/(m+n-1)]. c) The probability the first ball is red and the second is black is [n/(m+n)]*[m/(m+n-1)].

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A jar has m red balls and n black balls. we draw two balls from the jar. let B1 denote that the color of the first ball, and B2 denote the color of the second. let b denote black and r denote red. evaluate the following probabilities: a) P(B1=r) b) P(b2=b|B1=r) c) P(B1=r,B2=b) d) P(B1=b,B2=b) e) P(B2=b) f) P(B1=r|B2=b) Solution a) P(B1=r) = m/(m+n) b) P(B2=b|B1=r) = [m/(m+n)]*[n/(m+n-1)] c) P(B1=r,B2=b) = [n/(m+n)]*[m/(m+n-1)] d) P(B1=b,B2=b) = [n/(m+n)]*[(n-1)/(m+n-1)] e) P(B2=b) = [n/(m+n)]*[(n-1)/(m+n-1)] + [m/(m+n)]*[n/(m+n-1)] f) P(B1=r|B2=b) = [n/(m+n)]*[m/(m+n-1)]

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A jar has m red balls and n black balls. we draw two balls from the .pdf

  • 1. A jar has m red balls and n black balls. we draw two balls from the jar. let B1 denote that the color of the first ball, and B2 denote the color of the second. let b denote black and r denote red. evaluate the following probabilities: a) P(B1=r) b) P(b2=b|B1=r) c) P(B1=r,B2=b) d) P(B1=b,B2=b) e) P(B2=b) f) P(B1=r|B2=b) Solution a) P(B1=r) = m/(m+n) b) P(B2=b|B1=r) = [m/(m+n)]*[n/(m+n-1)] c) P(B1=r,B2=b) = [n/(m+n)]*[m/(m+n-1)] d) P(B1=b,B2=b) = [n/(m+n)]*[(n-1)/(m+n-1)] e) P(B2=b) = [n/(m+n)]*[(n-1)/(m+n-1)] + [m/(m+n)]*[n/(m+n-1)] f) P(B1=r|B2=b) = [n/(m+n)]*[m/(m+n-1)]