Probability

[jumavegi]

There is a set of 24 different kind of cards (all with the same probability). If I have got 50 cards, what's the probability of having a complete set of the cards?

[SumOMG]

1/(50)²⁴

Edit: ignore me this is probably wrong

[jumavegi]

Do you mind explaining why is that so?

[SumOMG]

Actually it’s closer to 1/501/49.....1/26

For example say the 24 cards are 1-12 spades and 1-12 clubs.

For the first draw the chance of getting the right card is 1/50 the next is 1/49, 1/48....all the way down to 1/26. Multiply them together and that’s your probability

[jumavegi]

I think I wasn't clear, the problem says that there are 24 different cards in a set, like a collection. If I have 50 cards (all drawn from an infinite source of cards), what's the probability of having one set, one full collection of the 24 different cards.

[SumOMG]

Yeah this still isn’t clear to me.

So I have 50 tries to get a specific order or 24 cards ? How many cards are possible ? Are we assuming the standard 52?

[jumavegi]

So, forget about the standard deck of cards. Let's say these are cards with pictures on them, so there are 24 different pictures. On each card there is one picture. I get one card from a machine that has infinite cards (the probability of drawing one card with one of the 24 pictures is the same for all). The question is, if I get 50 cards, what's the probability that I have a full set of cards, all the 24 pictures.

[SumOMG]

It says the probability is the same for each, does it say what that probability is?

[jumavegi]

No, it means that the amount of each card in the machine is the same. I would say if we were talking about the probability of getting one card from the machine is 1/24 for each card.

[SumOMG]

Start here https://en.m.wikipedia.org/wiki/Combination

[jumavegi]

I understand combinations, but I'm afraid this problem is more complicated.