A box contains $10$ red balls and $15$ green balls. If two balls are drawn in succession then the probability that one is red and other is green is

The correct option is B

$\frac{1}{2}$

Explanation for the correct answer:

Step 1: Sample space and event

Number of red balls $=10$

Number of green balls $=15$

Total number of balls $=25$

The sample space is drawn two balls from total number of balls

$$\begin{gathered} {=}^{25}{C}_2 \\ =\frac{25\times 24}{1\times 2} \\ =300 \end{gathered}$$

The event is drawing a red ball and a green ball in succession = ${}^{10}{C}_1{\times }^{15}{C}_1$

Step 2: Finding the probability

Thus the probability that one is red and other is green, P(e)

$$\begin{gathered} =\frac{{}^{10}{C}_1{\times }^{15}{C}_1}{300} \\ =\frac{10\times 15}{300} \\ =\frac{1}{2} \end{gathered}$$

Hence, option (B) is the correct answer.