Question

A changes16. By accident, 6 burned out bulbs have been mixed in with 16 good ones, Ken is replacing old bulbs in his house. If he selects two bulbs at random from the box of 22, what is theprobability they both work?

Answer 1

This is a combination problem. There are 22 bulbs present in the box and 16 of them are good ones. If we were to pick one good bulb out of 22, we have the probability

$P=\frac{16}{22}$

After picking the first good bulb, there are 15 remaining bulbs and there are a total of 21 remaining bulbs. Hence, the probability for picking a good bulb in this case is

$P=\frac{15}{21}$

The overall probability of getting two bulbs at random from the box of 22 will be the product of these two probabilities. We have

$P=\frac{16}{22}\times\frac{15}{21}=\frac{40}{77}$

Answer: P(both work) = 40/77