An urn contains 500 red marbles and 700 white ones. a. Use the hypergeometric distribution to find the probability of se...

Question

Question

An urn contains 500 red marbles and 700 white ones.

a. Use the hypergeometric distribution to find the probability of selecting 4 white marbles out of 5 selected without replacement

Answer 1

Answer #1

Probability mass function(pmf) for a discrete random variable(X) with hypergeometric distribution:

$PX (r) = P(X = z) = (m) (mm)$

Given: N=700+500=1200, n=5, m=700, x=4, N-m=500, n-x=5-4=1

In the question is is asked to find the probability of of selecting 4 white marbles out of 5.

$px (4) = P(X = 4) = (L) () (120$

4! (700-4). (500-1)! 0.2411686475 5! (1200-5)!

$0 500! 1200! 5! 1195!$

700+699 698+697 500 1.3 1200 1199 1198 1197*1196 5*4 3 2 1

0.2411686475

This is the probability of selecting 4 white marbles out of 5 without replacement.

Answer 2

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