There are 3 boxes in front of you each containing 6 coins On

There are 3 boxes in front of you, each containing 6 coins. One box contains all silver

coins; one box contains all gold coins; and one box contains half gold and half silver coins.

You randomly choose a box, take a coin from it, and place the coin in your pocket (not back

into the box). Given that the coin you took from the box is gold, what is the conditional

probability that you will pull out another gold coin if you reach into the same box?

I box -- 6 silver coins

II box -- 6 gold coins

III box -- 3 gold and 3 silver coins.

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A - The coin is gold

B1 - coin is from first box, B2 - coin is from second box, and B3 - coin is from III box.

C- prob that you reach the same box.

P(AB1) =0 P(AB2) =1/3 and P(AB3) = 1/6

P(A) =1/3+1/6 = 1/2

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P(B1/A) = P(AB1)/P(A) = 0

P(B2/A) = P(AB2)/P(A) = 1

P(B3/A) = 1/2

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Conditional prob to pull out another gold coin

= Reaches ii box draws gold coin and the first coin taken from ii box + Reachs III box and draws gold coin and the first coin taken from iii box

= 1/3(5/6)(1) + 1/3(2/6)(1/2)

= 5/18+ 1/12

= (30+12)/144 = 7/24