# Probability mass function

• Jan 31st 2010, 05:11 PM
Anonymous1
Probability mass function
Suppose we draw three balls out of an urn that contains 15 balls numbered 1 to 15. Let X be the largest number drawn. Find the probability function of X.

What I've got:
$\displaystyle For i>2, P(X=i) = \frac{(i-1)}{15}\times\frac{(i-2)}{14}\times\frac{1}{13}$

IDK just something feels wrong. Any help?

Thanks
• Jan 31st 2010, 07:37 PM
matheagle
I don't get that result.
I would do it via chooses...

$\displaystyle P(X=15)={{1\choose 1}{14\choose 2}\over {15\choose 3}}$

and $\displaystyle P(X=14)={{1\choose 0}{1\choose 1} {13\choose 2}\over {15\choose 3}}$

and $\displaystyle P(X=13)={{2\choose 0}{1\choose 1} {12\choose 2}\over {15\choose 3}}$

and $\displaystyle P(X=12)={{3\choose 0}{1\choose 1} {11\choose 2}\over {15\choose 3}}$

From this you can derive $\displaystyle P(X=x)$, which is three times your answer

$\displaystyle P(X=x)={{15-x\choose 0}{1\choose 1} {x-1\choose 2}\over {15\choose 3}}$

$\displaystyle ={3(x-1)(x-2)\over (15)(14)(13)}={(x-1)(x-2)\over (5)(14)(13)}$