Probability fundamentals + DSA Arrays/Hashing kickoff

Interview questions to prep

1. Compare hash-set O(n)/O(n) vs sort-and-scan O(n log n)/O(1) — when do you pick each?
2. What if the array doesn't fit in memory — how would you detect duplicates with limited RAM?

Interview questions to prep

1. Compare sorting (O(n log n)) vs counting-array (O(n), 26 buckets) — when do you pick each?
2. What if the strings include Unicode — does your counting-array still work?

Interview questions to prep

1. Walk through the brute-force O(n²), then explain how the hash map drops it to O(n).
2. What if the array is sorted — can you do better in space (two-pointer, O(1))?
3. What if duplicates are allowed and you need ALL pairs, not just one?

Interview questions to prep

1. What's the difference between joint, marginal and conditional probability — give a worked example?
2. When is independence the same as conditional independence? Why does the distinction matter for Naive Bayes?
3. Explain the law of total probability with a churn-prediction example.

Interview questions to prep

1. Walk through Bayes on a screening test (1% prevalence, 95% sensitivity, 90% specificity) — why is positive predictive value still low?
2. How would you use Bayes to update belief during an A/B test as data arrives?
3. When does using a strong prior hurt vs help in production ML?

Interview questions to prep

1. Two children: at least one is a girl. What's the probability the other is also a girl? Defend your answer.
2. Why is P(disease|positive) ≠ sensitivity in general?
3. Explain the base-rate fallacy with a hiring or fraud example.