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Two coins are available, one fair and the other two headed. Choose a coin and toss if once assume that the unbiased coin is chosen with probability 34.  Given that the outcome is head, the probability that the two-headed coin was chosen is

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Detailed Solution

P(F)=34,P(T)=1-34=14F→ Fair coin, T→ Two headed, H→ Head occurs ∴P(T/H)=P(H/T)·P(T)P(H/T)·P(T)+P(H/F)·P(F) [Using Baye's theorem] =1·141·14+12·34=25
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