If two fair coins are flipped and at least one of the outcomes is known to be a head What is the pro...........

Mathematics (NDA) Probability

If two fair coins are flipped and at least one of the outcomes is known to be a head . What is the probability that both outcomes are heads?

1/5

1/3

2/3

5/7

Let A be the event head in one coin

B be the event of the head in the second coin

The required probability is

P(A?B |A?B) =p{(A?B)?(A?B)}/p(A?B)

=p(A?B)/p(A?B)

P(A?B)=p(both coin heads)

=p(H,H)=1/4

P(A?B)=p(at least one head)

P(HH,HT,TH)=3/4

So required probability=1/4/3/4 =1/3

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