Math CentralQuandaries & Queries


Question from Danielle, a student:

A box contains 3 defective lights and 5 non-defective lights. The lights are tested one at a time without replacement. What is the probability that the 3 defective bulbs will be found in the first 3 tests?

is it 1/56 by chance?

Hi Danielle.

What is the probability that the first bulb is defective? It is 3 in 8.

If that occurs, then there is a 2 in 7 chance the second bulb chosen is defective and a 1 in 6 chance that the third bulb chosen is defective.

The chance therefore, that all three happen is (3/8)times(2/7)times(1/6) which is indeed 1/56.

Good thinking!
-Stephen La Rocque.

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