A bag contains 12 white and 18 black balls. Two balls are drawn in succession without replacement. What is the probability that first is white and second is black?

Answer: Option D

The probability that first ball is white:
$$\begin{array}{rl}& =\frac{{}^{12}{C}_1}{{}^{30}{C}_1}\\ & =\frac{12}{30}\\ & =\frac{2}{5}\end{array}$$
Since, the ball is not replaced; hence the number of balls left in bag is 29.
Hence, the probability the second ball is black:
$$\begin{array}{rl}& =\frac{{}^{18}{C}_1}{{}^{29}{C}_1}\\ & =\frac{18}{29}\end{array}$$
Required probability,
$$\begin{array}{rl}& =\left(\frac{2}{5}\right)\times \left(\frac{18}{29}\right)\\ & =\frac{36}{145}\end{array}$$