Find the probability they both function properly.

Question

In a box of 12 light bulbs, it is known that 5 of them are defective. That is, 5 are defective and 7 function properly. We select 2 bulbs from the bag at random, without placement.

Answer 1

n = 12 light bulbs in the box (5 are defective and 7 are working)

The probability that the light bulb is working is 7/12.

The probability that the light bulb is defective is 5/12.

We need to use the multiplication rule for probabilities. Keep in mind that the 1st light bulb is not replaced. These two events will be dependent.

P(1st light bulb working) = 7/12

P(2nd light bulb working | 1st light bulb working) = 6/11.

P(Both light bulbs working) = (7/12)*(6/11) = 42/132 = 21/66 = 7/22 ≈ 0.3182

The probability that both light bulbs are function properly is about 0.3182.