If a fair coin is tossed four times, what is the probability of obtaining at least one head?
-
A.
(frac{1}{2}) -
B.
(frac{1}{4}) -
C.
(frac{13}{16}) -
D.
(frac{15}{16})
Correct Answer: Option D
Explanation
P(at least one head) = 1 – P(4 tails)
Let (p = frac{1}{2}) = probability of head and (q = frac{1}{2}) = probability of tail.
((p + q)^{4} = p^{4} + 4p^{3}q + 6p^{2}q^{2} + 4pq^{3} + q^{4})
P(4 tails) = (q^{4} = (frac{1}{2})^{4} = frac{1}{16})
P(at least one head) = (1 – frac{1}{16} = frac{15}{16})