Products from a certain machine are too large 15% of the time. What is the probability that in a run of 20 parts, 5 are too large?

1 Answer
Teddy
Jun 25, 2018

C_5^20(.15)^5(.85)^15~~.103

Explanation:

The probability that 5 parts are too large is .15xx.15xx.15xx.15xx.15=(.15)^5 and since 5 parts are too large, the other 15 are of acceptable size with probability (1-.15)^15. Since any 5 parts can be too large in no particular order, there are C_5^20 ways to do this, so the probability that exactly 5 parts are too large is C_5^20(.15)^5(.85)^15~~.103.

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