You have an equal chance of receiving 1 of 4 prizes in a cereal box. Predict how many cereal boxes you would need to buy in order to win at least one of every prize.
The Attempt at a Solution
I have no idea whatsoever of how to solve this problem. At first glance it seems like it's 16 but is it really? I've asked some friends and one of them says that it's 256 because:
P(A and B and C and D) = P(A) x P(B) x P(C) x P(D) = 1/4 to the power of 4
But I'm not sure it's right because even though the probability is higher, it's still indefinite it's not a 100% chance that you will receive all 4 prizes.