Hi, I have been stuck with this example for quite a while now. The question is as follows:

A customer entering a bicycle store will buy a new bike with a probability of 10% and will buy bicycle accessories with a probability of 65%. With a probability of 30% a customer will not purchase anything.

(a) Find the probability that a customer will buy both a new bike and bicycle accessories.

and (b) Find the probability that a customer will only buy a bike.

I have done similar questions before however with this question I don't quite understand what to do with.

For part (a) I did the following:

A = buy a bike. P(A) = 0.1

B = buy bike accessories. P(B) = 0.65

Then I tried to use the formula:

P(A u B) = P(A) + P(B) - P(A n B) but I don't know how I would find P(A n B).

In the end I got a value of 0.685 but don't think its correct.

Thanks