Question

A fair coin is flipped four times. What is the probability that tails occurs exactly 4 times if it is known that tails occurs at least twice

Answer 1

P(tail) = 1/2 = 0.5

n = 4

This is a binomial distribution

P(X = x) = 4Cx * 0.5^x * (1 - 0.5)^4-x

P(X > 2) = P(X = 2) + P(X = 3) + P(X = 4)

              = 4C2 * 0.5² * 0.5² + 4C3 * 0.5³ * 0.5¹ + 4C4 * 0.5⁴ * 0.5⁰

              = 0.6875

P(X = 4) = 4C4 * 0.5⁴ * 0.5⁰ = 0.0625

P(X = 4 | X > 2) = P(X = 4 and X > 2) / P(X > 2)

                          = P(X = 4) / P(X > 2)

                          = 0.0625 / 0.6875

                          = 0.0909 or 1/11