The numbers 1 to 15 are placed in a hat, and a number is selected. What is the probability that the number is 4 given it is known to be an even number?

Answer 1

sounds like conditional probabilty

Prog(A|B) , (read as the prob of A, given B)
= prob(A AND B)/prob(B)

prob(A and B) = 1/15
prob(B) = 7/15

prob( as stated) = (1/15) / (7/15)
= 1/7

(of course, since the 4 is one of the 7 even numbers from 1 - 15)