Question

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

• A. $\frac{2}{7}$
• B. $\frac{1}{7}$
• C. $\frac{5}{7}$
• D. $\frac{3}{7}$

Answer 1

Answer: (D)

Let $E$ and $F$ denote respectively the events that first and second ball drawn are black. We have to find $P(E \,\cap\, F)$ or $P(FF)$.
Now, $P(E) = P$(black ball in first draw) $=\frac{10}{15}$
$P\left(F | E\right) =\frac{9}{14}$
By multiplication rule of probability, we have
$P\left(E \cap F\right) = P\left(E\right).P\left(F|E\right)$
$ = \frac{10}{15}\times\frac{9}{14} = \frac{3}{7}$