If a fair coin is tossed four times, what is the probability of obtaining at least one head?
Take Free Practice Test On 2026 JAMB UTME, Post UTME, WAEC SSCE, GCE, NECO SSCE
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) = \(1 - \frac{1}{16} = \frac{15}{16}\)
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) = \(1 - \frac{1}{16} = \frac{15}{16}\)