There are three coins. One is two - headed coin (having head on both faces), another is biased coin that comes up heads 75% of the times the third is also a biased coin that comes up tail 40% of the times. One of the three coins is chosen at random and tossed, and it shows heads. What is the probability that it was the two - headed coin?
Given:
Coin 1 has heads on both sides
Coin 2 and 3 are biased coins
Let us assume U1, U2, U3 and A be the events as follows:
U1 = choosing coin 1
U2 = choosing coin 2
U3 = choosing coin 3
A = getting head on tossing the coin
We know that each coin is most likely to choose. So, probability of choosing a coin will be same for every coin.
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From the problem:
⇒ P(A|U1) = P(getting head on tossing coin 1)
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⇒ P(A|U2) = P(getting head on tossing coin 2)
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⇒ P(A|U3) = P(getting head on tossing coin 3)
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Now we find
P(U1|A) = P(The head we get after is from tossing coin 1)
Using Baye’s theorem:
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∴ The required probability is 
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