Interview Q&A / Aptitude

1. A bag has 5 red and 3 blue balls. Two balls are drawn at random without replacement. What is the probability that both are red?

   5/14. First red: 5/8. Second red, given the first was red: 4/7. Multiply: 5/8 x 4/7 = 20/56 = 5/14. Using combinations: C(5,2)/C(8,2) = 10/28 = 5/14.

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2. A hits a target 3 times in 5 shots and B hits it 2 times in 4 shots. If both fire once, what is the probability that the target is hit?

   4/5. P(A hits) = 3/5, P(B hits) = 1/2. The target is missed only if both miss: 2/5 x 1/2 = 1/5. So P(hit) = 1 - 1/5 = 4/5.

   BeginnerQuick answer1 min read
3. A number is picked at random from 1 to 50. What is the probability that it is divisible by 3 or 5?

   23/50. Multiples of 3: 16. Multiples of 5: 10. Multiples of both (15, 30, 45): 3. By inclusion-exclusion, 16 + 10 - 3 = 23 favourable numbers out of 50.

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4. How do you convert odds in favour or odds against into a probability?

   Odds in favour a : b means a favourable outcomes for every b unfavourable, so the probability is a/(a + b). Odds against a : b mean probability b/(a + b). Odds in favour 3 : 5 give P = 3/8; odds against 7 : 3 give P = 3/10.

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5. What is the probability that a randomly chosen leap year has 53 Sundays?

   2/7. A leap year has 366 days = 52 weeks + 2 extra days. Those 2 consecutive days can be any of 7 pairs (Mon-Tue, ..., Sun-Mon), and 2 of them include a Sunday.

   BeginnerQuick answer1 min read