A bag contains 4 red, 5 blue and 6 green balls. Three balls are drawn without replacement. What is the probability that exactly two of them are red and one is green?

Step-by-step solution

1. Total balls = 4+5+6 = 15.
2. Total ways to choose 3 balls from 15 = C(15,3).
3. Ways to choose 2 red balls from 4 = C(4,2).
4. Ways to choose 1 green ball from 6 = C(6,1).
5. Favourable ways = C(4,2) × C(6,1) = 6 × 6 = 36.
6. Probability = favourable ways / total ways = 36 / C(15,3) = 36/455.

Concept tested: Hypergeometric probability.

Published 29 August 2026 · How this solution was prepared and checked

Related questions

• 1 A standard deck has 52 cards. What is the probability of drawing a face card (Jack, Queen or King)?
• 2 Two standard dice are rolled. What is the probability that the sum of the two numbers is at least 8?
• 3 The continuous random variable Y has probability density function f(y)=k,y for 0le yle2 and f(y)=0 elsewhere. Find the value of k and the expected value E[Y].
• 4 For the system x+2y-z=3, 2x+4y-2z=6, 3x+6y-5z=2, find the rank of the coefficient matrix and the augmented matrix and state whether the system is consistent. If it is consistent, give the solution.
• 5 A bakery makes cakes and pastries. The profit is ₹40 per cake and ₹30 per pastry. The resources are 2 hours of baking, 4 hours of packaging and 10 units of flour. Each cake needs 0.5 h baking, 0.2 h packaging, 3 units flour. Each pastry needs 0.3 h baking, 0.4 h packaging, 2 units flour. Using the graphical method, what is the maximum profit and how many cakes and pastries should be produced?
• 6 A firm produces product A and product B. 1 unit of A requires 1 unit of resource 1 and 3 units of resource 2. 1 unit of B requires 4 units of resource 1 and 2 units of resource 2. Daily availability: resource 1 = 20 units, resource 2 = 30 units. Profit per unit: A = ₹50, B = ₹60. Using the simplex method, find the maximum profit.