Probability-choose without replacement

I need some help at the following exercise...
We have a container that contains r balls that have numbers 1,...,r. We choose at random n of them without replacement. Let Y be the greatest and Z the smallest of the numbers of the balls we chose. Which are the probabilities P(Y<=y) and P(Z>=z)???

Reply 1

ghostwalker

17

Original post by mathmari

I need some help at the following exercise...
We have a container that contains r balls that have numbers 1,...,r. We choose at random n of them without replacement. Let Y be the greatest and Z the smallest of the numbers of the balls we chose. Which are the probabilities P(Y<=y) and P(Z>=z)???

Considering your first one, P(Y<=y).

Since Y is the greatest no. of the balls chosen. This can be paraphrased as "What is the probability that all n balls chosen are less than or equal to y".

Is that sufficient for you to complete it?

Edit: Corrected - had strict inequalities, when it should have been <=.