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Suppose a box contains three cards, one with both sides white, one with both sides black, and one with one side white and the other side black. If you pick a card at random, and the side facing you is white, then the probability that the other side is white is $1/2$.

3 Answers

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3 votes

1 card both side white

1 card both side black

1 card 1 side white 1side black

from these 3 cards probability of choosing any one card is 1/3

Now while 1 side of the card is white , then the probability of other side also white

By Baye's theorem

1/3*P(W) /(1/3*P(W) +1/3 *P(B))

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

=1/2 [Proved]

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Pls correct me if i am wrong

 

Given - selected white face  = 1/3*1 + 1/3*1/2

To calculate other side probability is white is 1/2 => 1/3*1/2  /  (1/3*1 + 1/3*1/2)  = > 1/3
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It is a case of conditional probability.

Probability of getting a white side = 3/6 = 1/2 (This is because we have total 6 faces. Out of them, 3 are white and 3 are black)

Given that one side is white, the probability that the other face is also white = (1/3) / (1/2) = 2/3

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