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If a fair coin is tossed four times, what is the probabil...

If a fair coin is tossed four times, what is the probability of obtaining at least one head?

A.

12

B.

14

C.

1316

D.

1516

Correct answer is D

P(at least one head) = 1 - P(4 tails)

Let p=12 = probability of head and q=12 = probability of tail.

(p+q)4=p4+4p3q+6p2q2+4pq3+q4

P(4 tails) = q4=(12)4=116

P(at least one head) = 1116=1516