Q15 of 249 Page 32

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.


⇒


⇒


⇒


From the problem:


⇒ P(A|U1) = P(getting head on tossing coin 1)


⇒


⇒ P(A|U2) = P(getting head on tossing coin 2)


⇒


⇒ P(A|U3) = P(getting head on tossing coin 3)


⇒


Now we find


P(U1|A) = P(The head we get after is from tossing coin 1)


Using Baye’s theorem:


⇒


⇒


⇒


⇒


⇒


∴ The required probability is .


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