Q.10 You are given three coins: one has heads on both faces, the second has tails on both faces, and the
third has a head on one face and a tail on the other. You choose a coin at random and toss it, and it
comes up heads. The probability that the other face is tails is
(A) 1/4 (B) 1/3 (C) 1/2 (D) 2/3
In this question they have given answer (B) as 1/3. We can get B if we take
P(C1) = 1/3, P(C2) = 1/3,P(C3) = 1/3
Where C1 has both head / tail & C2 has Head/Head, C3 has tail/tail.
Issue is that if we know that we have got heads , we can actually eliminate P(C3) , we can take it as 0.
Because it is given that we get Head when we toss it. (C3 can't generate head)
If we consider P(C1) = 1/2, P(C2) = 1/2 & P(C3) = 0 then answer I get is (D) 2/3 which is wrong as per GATE key. So please answer the question & Also let me know why should we consider C3 , if we know surely that coin is not C3.