Question:
Suppose you have two coins which appear identical in your pocket. You know that one is fair and one is 2-headed. If you take one out, toss it and get a head, what is the probability that it was a fair coin?
Solution:
Let’s consider
E1 = Event that the coin is fair
E2 = Event that the coin is 2 headed
And H = Event that the tossed coin gets head.
Now,
P(E1) = ½, P(E2) = ½, P(H/E1) = ½, P(H/E2) = 1
Using Baye’s Theorem, we get
Therefore, the required probability is 1/3.
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