We will be using the fact that
, where
is the probability that the first bulb works and
is the probability that the second bulb works.
The probability that the first bulb works is
. However, when we take one out (given that the first bulb works) we now have 19 working bulbs and 4 bad ones. This means that the probability that the second bulb works is
.
Now, we can find our final probability:
