Question

A coin is flipped 15 times. Let X be the number of flips in which we see a head.

What is the probability that we see a head in exactly 11 of the 15 flips?

Answer 1

4.17%

Explanation:

P = nCr pʳ qⁿ⁻ʳ

where n is the number of trials,

r is the number of successes,

p is the probability of success,

and q is the probability of failure (1−p).

Here, n = 15, r = 11, p = ½, and q = ½.

P = ₁₅C₁₁ (½)¹¹ (½)¹⁵⁻¹¹

P = 1365 (½)¹¹ (½)⁴

P = 1365 (½)¹⁵

P ≈ 0.0417