Question

Each of 3 boxes identical in appearance has 2 drawers. Box A has a gold coin in each drawer. Box B has a silver coin in each drawer while Box C contains a gold coin in one drawer and a silver coin in the other. A box is chosen one of its drawers is opened and a gold coin is found. a) What is the probability that the other drawer contains a silver coin b) What is the probability that the box chosen was Box A? Box B? Box C?

Answer 1

P(gold coin)= P(box A and gold coin)+P(box B and gold coin)+P(box C and gold coin)

=(1/3)*(1)+(1/3)*(0)+(1/3)*(!/2)=1/2

a)

P(other drawer has silver given gold coin) =P(box C and gold coin)/P(gold coin) =(1/3)*(1/2)/(1/2) =1/3

b)

P(Box A|gold coin)=P(box A and gold coin)/P(gold coin) =(1/3)*(1)/(1/2)=2/3

P(Box B|gold coin)=P(box B and gold coin)/P(gold coin) =(1/3)*(0)/(1/2)=0

P(Box C|gold coin)=P(box C and gold coin)/P(gold coin) =(1/3)*(1/2)/(1/2)=1/3