Question

An urn contains 10 black and 5 white balls. Two balls are drawn from the urn one after the other without replacement. What is the probability that both drawn balls are black?

Answer 1

Consider the given events.
A = A black ball in the first draw
B = A black ball in the second draw

$$\begin{gathered} \mathrm{Now}, \\ P\left(A\right)=\frac{10}{15}=\frac{2}{3} \\ P\left(B/A\right)=\frac{9}{14} \\ \therefore \mathrm{Required}\mathrm{probability}=P\left(A\cap B\right)=P\left(A\right)\times P\left(B/A\right)=\frac{2}{3}\times \frac{9}{14}=\frac{3}{7} \end{gathered}$$