Question

Two balls are drawn one after another without replacement from an urn containing 10 black balls and 5 white balls. What is the probability that both balls are black?

Options

• \[\frac{3}{7}\]

• \[\frac{9}{14}\]

• \[\frac{2}{3}\]

• \[\frac{1}{2}\]

Answer 1

Use \[P(E\cap F)=P(E)\cdot P(F\mid E)\]. Thus \[\frac{10}{15}\cdot\frac{9}{14}=\frac{3}{7}\], the probability that both balls are black.