Probability Quiz | Quantitative Aptitude MCQ Practice for IBPS AFO 2026

1

A box contains 25 music systems, out of which 16 are repaired and 9 are not repaired. Three music systems are chosen at random. Find the probability that at least one of them is repaired.

Solution & Explanation Required probability = 1 - P(none repaired) = 1 - C(9,3)/C(25,3) = 1 - 84/2300 = 2216/2300 = 554/575.

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2

There are 10 boys and 15 girls in a class. If 5 students are selected at random then what is the probability of selecting 2 boys and 3 girls?

Solution & Explanation P = C(10,2)×C(15,3)/C(25,5) = 45×455/53130 = 20475/53130 = 195/506.

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3

Four cards are drawn at random from a standard deck of 52 cards. Find the probability that at least 3 cards are hearts.

Solution & Explanation Favorable ways = C(13,3)×C(39,1) + C(13,4) = 11154 + 715 = 11869. Total ways = C(52,4) = 270725. Probability = 11869/270725 = 913/20825.

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4

A box contains x red balls, 8 black balls and 12 white balls. If the probability of picking a black ball is 1/3, then find the probability of picking a red ball at random.

Solution & Explanation P(black) = 8/(x+20) = 1/3 → x+20 = 24 → x = 4. Total = 24. P(red) = 4/24 = 1/6.

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5

In a UPSC interview, there are 5 male candidates and x female candidates. If two candidates are selected randomly, then the probability that both are female is 16.67%. What is the probability that at least one selected candidate is male?

Solution & Explanation Let the number of female candidates be x. Then C(x,2)/C(x+5,2) = 1/6. Solving gives x = 4. Total candidates = 9. Probability that both selected candidates are female = C(4,2)/C(9,2) = 1/6. Therefore, probability that at least one candidate is male = 1 − 1/6 = 5/6.

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Probability Quiz for IBPS AFO 2026

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