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A purse contains 3 coins C(1), C(2), C(3...

A purse contains 3 coins `C_(1), C_(2), C_(3)`. Where `C_(1)` is a fair coin, `C_(2)` is a biased coin with probability `(2)/(3)` of showing up head and `C_(3)` is a fake coin containing head on both sides. One of the coins is selected at random and tossed twice. If head is obtained on both the tosses, then the probability that the coin selected is not a fair coin is p. Then p =

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