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# Probability-choose without replacement watch

1. 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)???

2. (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)???

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 <=.
3. Is that {y choose n}/{r choose n}???????
4. (Original post by mathmari)
Is that {y choose n}/{r choose n}???????
You got it.
5. And how can I find the possibility P(Z>=z)???
6. (Original post by mathmari)
And how can I find the possibility P(Z>=z)???
Look back at how you did Y and have a think at how you could adapt the throught process for this situation, and the definition of Z.
7. Ok...Thank you very much!!!

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