What is the probability of picking for k times numbers (x1, ..., xk) lower than n in a bag containing N consecutive integer numbers assuming that once extracted the numbers are not put back in the bag?
Three examples:
- in a game of Bingo where N = 75, what is the probability of picking 15 (k) numbers lower than 20 (n)?
- what happens if in the example 1) N is 7500?
- in a card game where N = 52, what is the probability to pick once (k = 1) a card lower than 2 (n)?
Example 3) seems easy: $$P(x < 2) = \frac{4}{52}$$ where 4 are the four possible aces. But what about the other examples?