A box contains three coins two of them are fair and one two - heade...

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A box contains three coins two of them are fair and one two - headed. A coin is selected at random and tossed. If the head appears the coin is tossed again, if a tail appears, then another
\( \mathrm{P} \) coin is selected from the remaining coins and tossed.
(i) Find the probability that head appears twice.
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(ii) If the same coin is tossed twice, find the probability that it is two headed coin.
(iii) Find the probability that tail appears twice.
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