IIM B UG (B.Sc-Hons.)- Sample Paper 2026 · Quant & DI · Question 10

IIM B UG (B.Sc-Hons.)- Sample Paper 2026 question on Probability, with the answer and a step-by-step solution.

ProbabilityModern MathematicsMultiple choiceMedium
Bag I contains 2 red and 3 blue balls. Bag II contains 4 red and 1 blue ball. A bag is selected with equal probability, and two balls are drawn at random from it without replacement. Given that both balls are red, what is the probability that Bag II was selected?
  1. A
    \frac{6}{7}
  2. B
    \frac{4}{5}
  3. C
    \frac{3}{4}
  4. D
    \frac{2}{3}
Pick an option, then check.
Answer & solution

Answer: Option A

Each bag holds 5 balls, so two balls can be drawn from either in C(5, 2) = 10 ways.

Bag I has 2 red balls, so P(both red | Bag I) = C(2, 2) ÷ 10 = 1/10.

Bag II has 4 red balls, so P(both red | Bag II) = C(4, 2) ÷ 10 = 6/10.

Each bag is chosen with probability 1/2, so by Bayes' theorem:

P(Bag II | both red) = (1/2 × 6/10) ÷ (1/2 × 1/10 + 1/2 × 6/10).

The halves cancel, leaving 6 ÷ (1 + 6) = 6/7.

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