A student moving into a new flat buys a box of 20 light bulbs. Unknown to the student, exactly one of the bulbs is defective. Find:

b) Theconditionalprobability that the second bulb used is not defective,giventhat the first bulb used is not defective;

If the first bulb is not defective then you have 19 bulbs from which you can choose, and one of these is defective so the probability is .

This is the easy way to work it out but I am having trouble using the actual formula which may come in handy for other examples:

Let A be the event that the 2nd bulb is not defective.

Let B be the event that the 1st bulb is not defective.

Then

but how can you work out ?

So how can we work out that from what we are given?

I apologise for any offence my pedantry has caused