A hip joint replacement part is being stress-tested in a laboratory. The probability of successfully completing the test is 0.830. 7 randomly and independently chosen parts are tested. What is the probability that exactly two of the 7 parts successfully complete the test

0.00205

Step-by-step explanation:

This is binomial distribution problem.

Binomial distribution function is represented by

P (X = x) = ⁿCₓ pˣ qⁿ⁻ˣ

n = total number of sample spaces = 7

x = Number of successes required = 2

p = probability of success = 0.830

q = probability of failure = 1 - 0.83 = 0.17

P (X = 2) = ⁷C₂ 0.83² 0.17⁷⁻²

P (X = 2) = ⁷C₂ 0.83² 0.17⁵ = 0.00205