Question

Two balls are drawn in succession without replacement from an urn

containing 5 white balls and 6 black balls. Let B be the random variable

representing the number of black balls. Construct the probability distribution

of the random variable B.

Answer 1

$B=0:\;p=\frac{5}{11}*\frac{4}{10}=\frac{2}{11}.$

$B=1:\;p=\frac{5}{11}*\frac{6}{10}+\frac{6}{11}*\frac{5}{10}=\frac{6}{11}.$

$B=2:\;p=\frac{6}{11}*\frac{5}{10}=\frac{3}{11}.$