Question

From a box containing 2 apples, 2 peaches and 2 oranges, 3 fruits are drawn at

random. Let P be a random variable representing the number of oranges that occur. Construct a probability distribution.

Answer 1

$P(X=0)=\frac{4}{6}*\frac{3}{5}=\frac{2}{5}.$

$P(X=1)=\frac{2}{6}*\frac{4}{5}+\frac{4}{6}*\frac{2}{5}=\frac{8}{15}.$

$P(X=2)=\frac{2}{6}*\frac{1}{5}=\frac{1}{15}.$