Win All 4 Prizes in Cereal Box: Probability & Solution

[RainingIce]

Homework Statement

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
= 1/256
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.

 

[Chaos2009]

Right, from what you have told us, you cannot garuantee that you will win all four prizes no matter how many you buy, but you can predict the average amount of cereal boxes you will need to buy to win all four.

 

[qntty]

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
= 1/256

Yes that's the probability that you'll get all different prizes in the first four boxes, but that doesn't need to be the way you get at least one of four.


Have you posted the wording of the original problem? I'm guessing that it asked how many you'd have to buy to have an x% chance of getting all four.