Question

A bag contains 3 white, 4 red and 5 black balls. Two balls are drawn one after the other, without replacement. What is the probability that one is white and the other is black?

Answer 1

$$\begin{gathered} \text{Given:\hspace{0.17em}Box=}\left(\text{3 W+4R+5B}\right)\text{balls} \\ P\left(\text{one white and one black}\right)=P\left(\text{first white and second black}\right)+P\left(\text{first black and second white}\right) \\ =\frac{3}{12}\times \frac{5}{11}+\frac{5}{12}\times \frac{3}{11} \\ =\frac{15}{132}+\frac{15}{132} \\ =\frac{30}{132} \\ =\frac{5}{22} \end{gathered}$$