Interview Q&A / Data Science

1. How do you calculate conditional probability from a two-way table?

   P(A given B) is the count of A-and-B divided by the count of B. You restrict attention to the rows or columns where B is true and compute the share there. P(A given B) is not the same as P(B given A).

   BeginnerQuick answer1 min read
2. How do you find the probability of at least one success?

   Use the complement rule: P(at least one) = 1 - P(none). Computing the chance of nothing happening is much easier than adding up every way that something happens.

   BeginnerQuick answer1 min read
3. What is expected value, and how do you use it to judge a game or decision?

   Expected value is the probability-weighted average of all outcomes, the long-run average result of repeating a situation many times. A negative expected value means you lose on average, even if you sometimes win.

   BeginnerQuick answer1 min read
4. What is the difference between independent and mutually exclusive events?

   Independent events do not affect each other: P(A and B) = P(A) x P(B). Mutually exclusive events cannot happen together: P(A and B) = 0. Two events with non-zero probability cannot be both.

   BeginnerQuick answer1 min read
5. What is the difference between permutations and combinations?

   Permutations count arrangements where order matters; combinations count selections where order does not. Choosing r from n gives nPr = n!/(n-r)! ordered ways and nCr = n!/(r!(n-r)!) unordered ways.

   BeginnerQuick answer1 min read
6. When do you use the binomial distribution?

   Use it to count successes in a fixed number of independent trials, each with the same probability of success. The probability of exactly k successes in n trials is C(n,k) p^k (1-p)^(n-k).

   BeginnerQuick answer1 min read
7. How does Bayes theorem work? Explain with a medical test example.

   Bayes theorem updates a probability using new evidence: P(A|B) = P(B|A) x P(A) / P(B). It shows that a positive result from an accurate test can still mean a low chance of disease when the disease is rare.

   IntermediateQuick answer1 min read
8. What does the exponential distribution model?

   The exponential distribution models the waiting time until the next event when events arrive randomly at a constant rate. It is memoryless: the time already waited does not change the remaining wait.

   IntermediateQuick answer1 min read
9. What is the birthday paradox?

   In a group of just 23 people, the chance that two share a birthday is about 51%. It feels surprising because the number of pairs grows fast: 23 people form 253 pairs, each a chance for a match.

   IntermediateQuick answer1 min read
10. What is the difference between the Law of Large Numbers and the Central Limit Theorem?

    The Law of Large Numbers says the sample mean converges to the true mean as n grows. The Central Limit Theorem describes the shape and spread of the sample mean around that true value: approximately normal with SD sigma over root n.

    IntermediateQuick answer1 min read
11. What is the Poisson distribution, and what kind of data does it model?

    Poisson models the number of events in a fixed interval of time or space when events occur independently at a constant average rate. It has one parameter, the rate lambda, which is both its mean and its variance.

    IntermediateQuick answer1 min read