COMEDK 2025 Evening Solved Paper

Concept:Use the law of total probability with two cases based on the color of the first draw.Explanation:Consider the first draw: probability of green $P(\text{G}_1) = \frac{2}{7}$, and of red $P(\text{R}_1) = \frac{5}{7}$.If a green ball is drawn first, it is removed and one red is added.New composition: 6 red, 1 green → $P(\text{R}_2 \mid \text{G}_1) = \frac{6}{7}$.If a red ball is drawn first, it is removed and one green is added.New composition: 4 red, 3 green → $P(\text{R}_2 \mid \text{R}_1) = \frac{4}{7}$.Now apply total probability:$P(\text{R}_2) = P(\text{G}_1) \cdot P(\text{R}_2 \mid \text{G}_1) + P(\text{R}_1) \cdot P(\text{R}_2 \mid \text{R}_1) = \frac{2}{7} \cdot \frac{6}{7} + \frac{5}{7} \cdot \frac{4}{7} = \frac{12}{49} + \frac{20}{49} = \frac{32}{49}$.Answer:Option B. $\frac{32}{49}$