Interview Q&A / Aptitude

1. How do you solve probability questions on coins, dice and cards?

   Probability = favourable outcomes / total outcomes, when all outcomes are equally likely. List the sample space carefully. Two coins have 4 outcomes, two dice have 36, a deck has 52 cards. For "at least one" questions, use 1 minus the probability of none.

   IntermediateIn-depth4 min read
2. 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.

   BeginnerQuick answer1 min read
3. 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
4. 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.

   BeginnerQuick answer1 min read
5. 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.

   BeginnerQuick answer1 min read
6. 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
7. What is the probability that 4 randomly chosen people were all born on different days of the week?

   840/2401, about 0.35. The first person can be born on any day (7/7), the second on one of 6 other days, the third on 5, the fourth on 4: (7 x 6 x 5 x 4) / 7^4 = 840/2401.

   AdvancedQuick answer1 min read