Answer :

Given: let E_{1} be the event of choosing a two headed coin, E_{2} be the event of choosing a biased coin and E_{3} be the event of choosing an unbiased coin. Let A be the event that the coin shows head.

Then P (E_{1}) = P (E_{2}) = P (E_{3}) = 1/3

As we a headed coin has head on both sides so it will shows head.

Also P(A|E_{1}) = P (correct answer given that he knows) = 1

And P(A|E_{2}) = P (coin shows head given that the coin is biased)

And P(A|E_{3}) = P (coin shows head given that the coin is unbiased)

Now the probability that the coin is two headed, being given that it shows head, is P(E_{1}|A).

By using bayes’ theorem, we have:

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