Answer to Question #182893 in Statistics and Probability for xsamdanielx

Question #182893

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?


1
Expert's answer
2021-05-04T12:37:27-0400

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

Given n=10,p=0.8.n=10, p=0.8.


P(X=7)=(107)(0.8)7(10.8)107=0.2013P(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.



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