Question

Assume that X is a binomial random variable with n = 12 and p = 0.90. Calculate the following probabilities. (Do not round intermediate calculations. Round your final answers to 4 decimal places.

a.	P(X = 11)
b.	P(X = 10)
c.	P(X ≥ 10)

Answer 1

P(X = x) = 12Cx * 0.9^x * (1 - 0.9)^12-x

a) P(X = 11) = 12C11 * 0.9¹¹ * 0.1¹ = 0.3766

b) P(X = 10) = 12C10 * 0.9¹⁰ * 0.1² = 0.2301

c) P(X > 10) = P(X = 10) + P(X = 11) + P(X = 12)

                    = 12C10 * 0.9¹⁰ * 0.1² + 12C11 * 0.9¹¹ * 0.1¹ + 12C12 * 0.9¹² * 0.1⁰

                    = 0.8891