Probability - Conditional Probability and Bayesian Inference Interview Problems
Interview Experience
Round 1 ML / Probability
Problem
You are given several probability problems typical of ML Engineer and data science interviews. Solve each clearly, showing your reasoning.
Q1: A test for a disease has 99% sensitivity and 95% specificity. The disease affects 1% of the population. Given a positive test result, what is the probability the patient actually has the disease?
Q2: Two fair dice are rolled. Given that the sum is at least 9, what is the probability that at least one die shows a 6?
Q3: An ML model outputs a score in [0, 1]. You observe that it is well-calibrated: P(y=1 | score=p) = p. You have two predictions: 0.7 and 0.8. What is the probability that both underlying events occur?
Expected Reasoning
Q1: P(disease | positive)
= P(pos | disease) * P(disease) / P(positive)
= (0.99 * 0.01) / (0.99*0.01 + 0.05*0.99)
~= 16.7%
Follow-ups
- How does the base rate (disease prevalence) affect the PPV? What if prevalence drops to 0.1%?
- Explain the difference between frequentist and Bayesian interpretations of these answers.
- In a recommender model, calibration matters for ranking vs. revenue optimization differently. How?
- How do you detect and correct miscalibration in a deployed classification model?
Full Details
Round 1 ML / Probability
Problem
You are given several probability problems typical of ML Engineer and data science interviews. Solve each clearly, showing your reasoning.
Q1: A test for a disease has 99% sensitivity and 95% specificity. The disease affects 1% of the population. Given a positive test result, what is the probability the patient actually has the disease?
Q2: Two fair dice are rolled. Given that the sum is at least 9, what is the probability that at least one die shows a 6?
Q3: An ML model outputs a score in [0, 1]. You observe that it is well-calibrated: P(y=1 | score=p) = p. You have two predictions: 0.7 and 0.8. What is the probability that both underlying events occur?
Expected Reasoning
Q1: P(disease | positive)
= P(pos | disease) * P(disease) / P(positive)
= (0.99 * 0.01) / (0.99*0.01 + 0.05*0.99)
~= 16.7%
Follow-ups
- How does the base rate (disease prevalence) affect the PPV? What if prevalence drops to 0.1%?
- Explain the difference between frequentist and Bayesian interpretations of these answers.
- In a recommender model, calibration matters for ranking vs. revenue optimization differently. How?
- How do you detect and correct miscalibration in a deployed classification model?
About This Question
This is a candidate experience report from a stackadapt interview during the onsite round.
More Stackadapt Interview Questions
About Stackadapt Interview Reports
This question was reported by a candidate who interviewed at Stackadapt. LeakCode aggregates interview reports from 10+ sources, including 1Point3Acres, Glassdoor, LeetCode Discuss, Blind, Reddit, Indeed, and Nowcoder. Each report is translated where necessary, deduplicated against existing entries, and tagged by company, role, round type, and reporting date.
Use this question as one calibration data point, not a memorization target. Companies typically rotate their question pools every 2-4 months; the exact wording of a 2024 question may differ from what you encounter today. The underlying pattern, difficulty level, and follow-up depth at Stackadapt are the higher-signal extractions to take from this report.
For broader preparation context, the Stackadapt interview process typically includes a recruiter screen, one or two technical phone screens, and a 4-5 round on-site loop covering coding, system design (at L4+ levels), and behavioral. Reports tagged on LeakCode show the round-by-round distribution and typical difficulty calibration. To browse questions filtered by round type and seniority, use the company hub linked above.
How To Practice This Type of Question
Solve similar problems on LeetCode under timed conditions (25-35 minutes per medium difficulty). The goal is pattern recognition: recognize the underlying technique (sliding window, two-pointer, BFS, memoized recursion, etc.) within 60-90 seconds of reading. Strong candidates verbalize their hypothesis out loud before coding, then iterate based on feedback. Weak candidates dive into implementation immediately, lose time on the wrong approach, and run out of time for follow-ups.
Companies update their question pools every 2-4 months. The exact wording of any given question may have been retired by the time you interview. Focus your prep on the pattern, not the specific problem. The patterns that appear in Stackadapt reports consistently are the ones worth investing in; one-off niche problems are not.
During Your Stackadapt Round
Apply the standard interview round template: clarify requirements (2-3 minutes), state your approach out loud and confirm direction with the interviewer (3-5 minutes), code with narration (15-25 minutes), test with concrete examples including edge cases (5 minutes), discuss optimization or trade-offs if time permits (5 minutes). This template is universally accepted across FAANG and adjacent companies; deviating from it produces weaker interviewer feedback signal.
The single most predictive failure mode in Stackadapt reports tagged "no hire": not asking clarifying questions. Interviewers are explicitly trained to weight this. Strong candidates ask 3-5 clarifying questions even on problems that look obvious; weak candidates dive into code immediately. The clarifying-question check is often the first signal recorded in the interviewer's written notes.