Suppose you have two coins which appear identical
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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