Probability Quiz | Quantitative Aptitude MCQ Practice for IBPS AFO 2026

1

Bag A contains 7 White and 8 Black balls, while Bag B contains 6 White and 5 Black balls. If 5 balls are drawn at random from each bag, find the product of the probability that 3 White and 2 Black balls are drawn from Bag A and 2 White and 3 Black balls are drawn from Bag B.

Solution & Explanation For Bag A: P₁ = [C(7,3) × C(8,2)]/C(15,5) = 980/3003. For Bag B: P₂ = [C(6,2) × C(5,3)]/C(11,5) = 150/462 = 25/77. Required probability = P₁ × P₂ = (980/3003) × (25/77) = 500/4719.

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2

Neel, Nitin and Mukesh try to hit a target. Their probabilities of hitting the target are 3/7, 2/5 and 4/7 respectively. Find the probability that exactly two of them hit the target.

Solution & Explanation Required probability = (3/7)(2/5)(3/7) + (3/7)(3/5)(4/7) + (4/7)(2/5)(4/7) = 18/245 + 36/245 + 32/245 = 86/245. Since 86/245 is not among the options, the answer is None of these.

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3

In a class there are 12 boys and 8 girls. If a group of 3 students has to be made, then what is the probability of getting at least two girls in the group?

Solution & Explanation P(at least 2 girls) = P(exactly 2 girls) + P(exactly 3 girls). = [C(8,2)×C(12,1) + C(8,3)] / C(20,3) = [336 + 56] / 1140 = 392/1140 = 98/285.

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4

A bag contains x green and (x+1) red balls. If probability of drawing a red and a green ball from the bag simultaneously is 5/9, then find number of red balls in the bag.

Solution & Explanation Total balls = 2x + 1. Probability of drawing one green and one red ball simultaneously = [C(x,1) × C(x+1,1)] / C(2x+1,2) = x(x+1) / [(2x+1)x] = (x+1)/(2x+1) Given, (x+1)/(2x+1) = 5/9 ⇒ 9x + 9 = 10x + 5 ⇒ x = 4 Therefore, number of red balls = x + 1 = 5.

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5

A bag containing 24 balls has red, blue and green balls in the ratio of 2:3:1 respectively. Two balls are drawn at random from the bag, then what is the probability that both drawn balls are of red colour?

Solution & Explanation Red = 8, Blue = 12, Green = 4. P = C(8,2)/C(24,2) = 28/276 = 7/69.

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Probability Quiz for IBPS AFO 2026

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