(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. The process continues until all balls of one color are drawn. The probability that the last ball drawn is black is ( ).
(A) $\frac{3}{5}$
(B) $\frac{4}{7}$
(C) $\frac{1}{2}$
(D) $\frac{3}{7}$
(3) B Hint: The number of ways to draw all 7 balls is $\mathrm{C}_{7}^{3}=\mathrm{C}_{7}^{4}=35$, the number of ways to draw all 3 black balls is $\mathrm{C}_{6}^{3}=20$, thus the required probability is $\frac{20}{35}=\frac{4}{7}$.