3. A box contains 3 black balls and 4 white balls. Now, a ball is randomly drawn from the box each time, and the ball is not put back after it is drawn. Each ball has an equal chance of being drawn, until all balls of one color are drawn. What is the probability that the last ball drawn is black? ( ).
(A) $\frac{3}{5}$
(B) $\frac{4}{7}$
(C) $\frac{1}{2}$
(D) $\frac{3}{7}$
3. B.
There are $\mathrm{C}_{7}^{3}=35$ ways to draw all 7 balls, and there are $\mathrm{C}_{6}^{3}=20$ ways to draw all 3 black balls. Therefore, the required probability is $\frac{20}{35}=\frac{4}{7}$.