Answer to Question #4666 in Statistics and Probability for Elizabeth

Question

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.

Answer 1

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.