Thread: find probability mass function

1. find probability mass function

The contents of an urn are % blue, 4 red and 6 white balls. Consider the experiment: one chooses a ball from the urn records the color of the ball, puts it back; does this again, then again, then again. Let us assume that one is interested in the number of white balls that were chosen amongst the four balls chosen and let us call the variable "W". Find a probability mass function for "W" where the domain of the function is R( real numbers) and the codomain is R.

2. $\displaystyle f(W=w)=(\frac{6}{15})^w(\frac{9}{15})^{4-w}$

3. typo...there are 5 blue balls

4. How do i know it's summation =1 ? geometric series i would guess?

5. I am sorry to tell you but the first reply is mistaken.

It should be $\displaystyle P(W=n)=\dbinom{4}{n}\left(\dfrac{6}{15}\right)^n \left(\dfrac{9}{15}\right)^{4-n};~n=0,1,2,3,4$

The sum $\displaystyle \sum\limits_{n = 0}^4 {P(W = n)} = 1$ must be true because the total probability mass is 1.