Answer to Question #182893 in Statistics and Probability for xsamdanielx

Question

If there are 10 candidate materials that can be used for manufacturing a certain machine and the probability that each one leads to a machine that lasts at least 10 years is 0.8, what is the probability that exactly 7 of the machines will last at least 10 years?

Answer 1

Let $X=$ the number of machines: $X\sim Bin(n, p)$

Given $n=10, p=0.8.$

$$P(X=7)=\dbinom{10}{7}(0.8)^7(1-0.8)^{10-7}=0.2013$$

The probability that exactly 7 of the machines will last at least 10 years is 0.2013.