Question

By accident, six 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 the probability they both work?

Answer 1

We will assume that he does not replace the first one.

He needs to choose 2 good one from 16 good ones. How can he do this?

$\dbinom{16}{2}= \dfrac{16*15}{1*2}=120$

The total number of ways of choosing 2 lightbulbs [good or bad] is

$\dbinom{22}{2} = \dfrac{22*21}{2*1} = 231$

So the probability of getting a good light bulb is

$\boxed{\dfrac{120}{231}=\dfrac{40}{77}}$