Question

We are given three coins. One has heads on both faces, the second has tails on both faces, and the third coin has a head on one face and a tail on the other face. We choose one coin at random, toss it, and observe that the result is heads. What is the probability that the opposite face is tails?

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Answer #1

This is a case of Conditional Probability.

Let there be two events A and B. Event A denotes the probability of getting a head from the toss of three given coins. Event B is the event of the other side of the resultant coin in first toss being tails.

P(A|B)=P(AintersectionB)/P(B)

We know that P(AintersectionB)=1/3 (Since there’s only one coin that can both give heads and be tails on the opposite side).

And, P(B)=2/3 (Since there are 2 coins that can show tails on the opposite face)

Therefore, P(A|B)=(1/3)/(2/3)=1/2

.. Or, there is a very easy way to look at this answer. Given that you already got heads, now your sample space is only reduced to 2 coins (since the one with both sides tails can’t give heads). We are asked for the probability of the coin being the one with opposite sides. Therefore,

P=(No.of favourable Outcomes)/(Total no. of outcomes)=1/2

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