IBPS PO Prelims 23 Aug 2025 Shift 3 Solved Paper

Concept:Probability is the ratio of favorable outcomes to total outcomes; here, use complementary counting by subtracting the probability of drawing two balls of the same color from 1.Explanation:Total balls in the bag = $5 + 4 + 3 = 12$.Total ways to draw any 2 balls from 12 without replacement = $^{12}C_2 = \frac{12 \times 11}{2 \times 1} = 66$.Find the number of ways to draw 2 balls of the same color:Red: $^{5}C_2 = 10$; Blue: $^{4}C_2 = 6$; Green: $^{3}C_2 = 3$.So same-color combinations = $10 + 6 + 3 = 19$.Probability that both balls are the same color = $\frac{19}{66}$.Therefore, probability that both balls are of different colors = $1 - \frac{19}{66} = \frac{66 - 19}{66} = \frac{47}{66}$.Verification by direct selection: Favorable ways = red-blue + blue-green + red-green = $(5 \times 4) + (4 \times 3) + (5 \times 3) = 20 + 12 + 15 = 47$.Thus, required probability = $\frac{47}{66}$.Answer:$\frac{47}{66}$, which matches option C.