Question #4666

The calibration of a filling machine broke, causing it to underfill 5 jars of jam. The jars were accidentally mixed in with 9 properly filled jars. All the jars look the same. 3 jars are chosen from the batch and weighed. What is the probability that exactly 2 jars are underweight?
Round your answer to 3 decimal places.

Expert's answer

We choose 3 jars from 5+9=14. In total we have 14!/(3!11!) = 364 different ways

to choose them.

2 jars must be underweight. So, we choose 2 from 5 in

5!/(2!3!) = 10.

We choose 1 jar from 9 properly filled - 9.

So, we get the

probability 9*10/364 = 0.247.

to choose them.

2 jars must be underweight. So, we choose 2 from 5 in

5!/(2!3!) = 10.

We choose 1 jar from 9 properly filled - 9.

So, we get the

probability 9*10/364 = 0.247.

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