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}(\binom32\binom40)/(\binom72)=\frac17&\text{for }x=0\\\\(\binom31\binom41)/(\binom72)=\frac47&\text{for }x=1\\\\(\binom30\binom42)/(\binom72)=\frac27&\text{for }x=2\\\\0&\text{otherwise}\end{cases}`