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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 $1/2$.
asked in Probability by Veteran (28.1k points)   | 51 views

1 Answer

+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]


answered by Veteran (49.7k points)  
How's the Bayes formula applied here? - the terms are not clear.
No sir I think it is clear

Because we already know one side is white

Then probability of other side white

It is a conditional probability :)
yes, bu that is intuition. We know only 2 coins are there with at least one face white. Try applying Bayes formula properly, you should not get 1/2 and this is a common mistake everyone makes in conditional probability.
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