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A fair coin is tossed 3 times. Find the probability of ob...

A fair coin is tossed 3 times. Find the probability of obtaining exactly 2 heads.

A.

18

B.

38

C.

58

D.

78

Correct answer is B

Let the probability of getting a head = p = 12 and that of tail = q = 12

(p+q)3=p3+3p2q+3pq2+q3

In the equation above, p3 and q3 are the probabilities of 3 heads and 3 tails respectively 

 while, p2q and pq2 are the probabilities of 2 heads and one tail and 2 tails and one head respectively.

Probability of exactly 2 heads = 3p2q=3(12)2(12)

= 38