Question

In a national basketball​ association, the top​ free-throw shooters usually have probability of about

0.80 of making any given free throw. Complete parts a through c.

c.

Find the probability that the player made all 10 free​ throws, 99 free​ throws, and more than 77 free throws.

The probability that the player made all

10 free throws is....

Answer 1

This is a binomial distribution.

n = 10

p = 0.8

P(X = x) = ¹⁰C_x * 0.8^x * (1 - 0.8)^10-x

a) P(X = 10) = ¹⁰C₁₀ * 0.8¹⁰ * 0.2⁰ = 0.1074

b) P(X = 9) = ¹⁰C₉ * 0.8⁹ * 0.2¹ = 0.2684

c) P(X > 7) = P(X = 8) + P(X = 9) + P(X = 10)

                  = ¹⁰C₈ * 0.8⁸ * 0.2² + ¹⁰C₉ * 0.8⁹ * 0.2¹ + ¹⁰C₁₀ * 0.8¹⁰ * 0.2⁰
                  = 0.6778