Question

Suppose that an unfair coin comes up heads 52.2% of the time. The coin is flipped a total of 19 times.

a) What is the probability that you get exactly 9 tails?

b) What is the probability that you get at most 17 heads?

Answer 1

It is a binomial distribution.

P(X = x) = nCx * p^x * (1 - p)^{n - x}

a) n = 19

P(tails come up) = 1 - 0.522 = 0.478

P(X = 9) = 19C9 * (0.478)^9 * (0.522)^10 = 0.1808

b) P(heads come up) = 0.522

P(X < 17) = 1 - P(X > 17)

                 = 1 - (P(X = 18) + P(X = 19) )

                 = 1 - (19C18 * (0.522)^18 * (0.478)^1 + 19C19 * (0.522)^19 * (0.478)^0)

                = 1 - 0.0001

                = 0.9999