IanStewart
Roughly half of the solutions in this thread are not correct (the ones that are multiplying two probabilities). The "rule"
P(A and B) = P(A) * P(B)
is only true when A and B are independent. So you can use that rule if you're rolling a die and then flipping a coin, say, because then the outcome of the first event has no influence on the outcome of the second. But if you're concerned with just a single event, like picking a single number from a set, you're absolutely never dealing with two independent events, so you can never use this rule (or at least not without risking a mistake).
You can see why this multiplication approach is not correct just by imagining a different set - say we pick one number from this list:
1, 2, 3, 4, 5, 6, 7, 8, 9, 10
and want to know if we pick a number that is both a multiple of 3 and a multiple of 5. Picking one number randomly from this set, the probability of picking a multiple of 3 is 3/10, and of picking a multiple of 5 is 1/5, but the probability of picking a number divisible by both 3 and 5 (so by 15) is not (3/10)(1/5) = 3/50. It is zero.
The solutions in this thread that are correct are those that are counting the number of multiples of 15 we have (there are six of them), and then dividing by the size of the set we're picking from (there are 90 numbers we're selecting from).
Thanks
IanStewart for correcting me. I had suggested two ways above. Now, one of them is incorrect.
I was lucky in this case as I got same answer both ways. Else I would have marked wrong answer.