1. ## [SOLVED] prob distribution

A drawer contains 8 brown socks and 4 blue socks. A sock is taken from the drawer at random, its color is noted and it is then replace. This procedure is performed twice more. If X is the r.v "the # of brown socks taken", find the prob distribution for X

Can somebody explain this question to me pls!tnX

2. I assume r.v. means random variable

So we have $\displaystyle P(brown) = \frac{8}{12} = \frac{2}{3}$

And $\displaystyle P(blue) = \frac{4}{12} = \frac{1}{3}$

The probability distribution will be as follows:

$\displaystyle P(X=0) = P(blue) \times P(blue) = [P(blue)]^2 = \left(\frac{1}{3}\right)^2$

$\displaystyle P(X=1) = P(blue) \times P(brown) + P(brown) \times P(blue) = 2 \times P(blue) \times P(brown)$$\displaystyle = 2 \times \frac{1}{3} \times \frac{2}{3}$

$\displaystyle P(X=2) = P(brown) \times P(brown) = [P(brown)]^2 = \left(\frac{2}{3}\right)^2$

And that's the probability distribution for X.