Question

A bing contains 3 red and 4 green balls. 2 balls are chosen at random, without replacement. Let the random variable X be the number of aren balls chosen.
Construct a probability distribution for table X.

Answer 1

Assuming "aren" is supposed to say "green":

$\mathbb P(X=x)=\begin{cases}\dfrac{\binom32\binom40}{\binom72}=\dfrac17&\text{for }x=0\\\\\dfrac{\binom31\binom41}{\binom72}=\dfrac47&\text{for }x=1\\\\\dfrac{\binom30\binom42}{\binom72}=\dfrac27&\text{for }x=2\\\\0&\text{otherwise}\end{cases}$