How to find the probability of collecting yogurt stickers?

Question

Probability theory

One of 50 unique stickers can be found on each yogurt. If you collect all 50 - you get a prize. Let's denote by X - the number of yogurts that you need to buy in order to successfully collect all the stickers. What is P(X=51) equal to? P - probability

Answer 1

According to the formula of combinations with repetitions, the total number of different combinations (how many ways can you choose 51 stickers from 50 unique ones) = 100!/(49!*51!). Now the question is, how many combinations, out of all of these, favor our event (that there are 50 unique ones)? it can also be verbally counted - 50 unique and one any, and which can be any - 50 options. That is, P(x=51)= 50/(100!/(49!*51!)) or 49!*50*51!/100!
In simple terms: out of 100!/(49!*51!) possible combinations, there are 50 when all unique stickers meet.

Answer 2

Tired by the end of the week, but I think the answer should be close to 1 * 49/50 * 48/50 * 47/50 * ... * 3/50 * 2/50 * 1/50.
Those. the probability of getting some particular sticker = 1/50. When none is available, any will do, then any but one, then any but two, and so on.
Just think about how to take into account the possibility of a single repetition of stickers (in conditions of 51, not 50), otherwise it’s very hard for me to think on Friday :)

Answer 3

Depends on the number of yogurts produced. If they were released by 51, then 100%.
Depends on the distribution of yogurt in stores. If yoghurts with one of the stickers were not sent to your store, then 0%.
Depends on the number of issued stickers of each type.

Answer 4

Let's denote by X - the number of yogurts that you need to buy in order to successfully collect all the stickers.

You yourself said that with X there will be P = 100% ("successfully collect all the stickers")
If you meant something else, then reformulate the problem unambiguously. And add the missing information (total number of yogurts, number of stickers of each type, etc.)