# Probability mass function

• March 30th 2008, 08:59 PM
Andreamet
Probability mass function
an urn contains 100 balls: 20 white, 30 black and 50 gray. SUpposed that 20 balls are chosen at random and without replacement. Let W,B, and G be the number of balls, respectibely. Calculate the probability mass function of B,W, and G
• March 31st 2008, 05:26 AM
mr fantastic
Quote:

Originally Posted by Andreamet
an urn contains 100 balls: 20 white, 30 black and 50 gray. SUpposed that 20 balls are chosen at random and without replacement. Let W,B, and G be the number of balls, respectibely. Calculate the probability mass function of B,W, and G

You have a multivariate hypergeometric distribution:

Pr(W = w, B = b, G = g) $= \frac{ {20 \choose w} {30 \choose b} {50 \choose g}}{{100 \choose 20}}$

where w + b + g = 20.

You could also build in the w + b + g = 20 restriction and write the pmf as:

Pr(W = w, B = b, G = g) $= \frac{ {20 \choose w} {30 \choose b} {50 \choose {20 - w - b} }}{{100 \choose 20}}$.

And, I hate to say it, but the jury question you posted a while ago will also follow a multivariate hypergeometric distribution since (I assume) there's no replacement after each juror is selected. The card one too - if there's no replacement. I've added a reply noting this to each of those threads.