I choose a random sample of 5 of 20 sofas and I find that all of them are more than $400. If only 10 of these sofas were supposed to be more than $400, what is the probability I would get 5 costing more than $400 in my sample of 5? What would that probability be if 11 of the sofas cost more than $400? Or 12 sofas costing more than $400?

A First Course in Probability (10th Edition)
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Chapter1: Combinatorial Analysis
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I choose a random sample of 5 of 20 sofas and I find that all of them are more than $400.

If only 10 of these sofas were supposed to be more than $400, what is the probability I would get 5 costing more than $400 in my sample of 5?

What would that probability be if 11 of the sofas cost more than $400? Or 12 sofas costing more than $400? 

Expert Solution
Step 1

Let 'n' be the total number of sofas = 20

A sample of 5 sofas is selected from a total of 20 sofas.

Let X be the number of sofas which costs more than $400 in a sample of 5 sofas selected.

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