The probability of picking a single bad brake is indeed
15/500 = 3%.
However, the probability of picking a bad brake followed by 3 good brakes is
15/500 * 485/499 * 484/498 * 483/497 = 2.75%
But the bad one could be drawn 1st, 2nd,3rd or 4th, so multiply by 4 -> 11.0% that one of the four is bad!
You can come mighty close just using the binomial distribution. In Excel that would be =BINOMDIST(1,4,0.03,FALSE) which gives 10.9% Binomial assumes that there is a 3% chance that the next is bad, no matter what the ones before were. Since the lot is large (500) and the sample is small (4), this approximation should worke pretty well.
I agree with roland_lu for the odds of all four being bad.
To wonder is to begin to understand.