Solve Probability and Logic Puzzles Under Interview Pressure
Problem: Probability and Logic Puzzles
This interview presents a series of distinct quantitative and logical reasoning puzzles. Candidates are expected to articulate their thought process, solve each problem, and discuss any underlying assumptions.
Puzzle 1: Car Arrival Probability
Given that the probability of observing at least one car in a one-hour interval is 0.99, what is the probability of observing at least one car in a half-hour interval?
Assume independent Poisson-like arrivals for the car problem.
Puzzle 2: Combined Work Rate
Crew A can complete a specific task in 6 days. Crew B can complete the same task in 8 days. If both crews work together, how many days will it take them to complete the task?
Assume that their work rates add linearly.
Puzzle 3: Battery Testing Strategy
You have 8 batteries, and exactly 4 of them are known to be working. A toy requires two working batteries to start. Design a strategy to find two working batteries using the minimum number of tests.
Each test involves selecting a pair of batteries and placing them in the toy. The test succeeds (the toy starts) only if both batteries in the pair are working. The goal is to find any two working batteries, not to identify all working or non-working batteries.
AI interview prep
Core dilemma
The central challenge is to demonstrate analytical rigor and problem-solving versatility across diverse quantitative domains (probability, rate problems, combinatorial optimization). Candidates must clearly articulate assumptions, apply appropriate mathematical models, and optimize for specific criteria (e.g., minimum tests) under pressure.
3 tradeoffs and 3 stress tests locked
Interview prep
Unlock the interviewer X-Ray rubric, tradeoff matrix, stress tests, clarifying questions, and key concepts.
Solve Probability and Logic Puzzles Under Interview Pressure
Problem: Probability and Logic Puzzles
This interview presents a series of distinct quantitative and logical reasoning puzzles. Candidates are expected to articulate their thought process, solve each problem, and discuss any underlying assumptions.
Puzzle 1: Car Arrival Probability
Given that the probability of observing at least one car in a one-hour interval is 0.99, what is the probability of observing at least one car in a half-hour interval?
Assume independent Poisson-like arrivals for the car problem.
Puzzle 2: Combined Work Rate
Crew A can complete a specific task in 6 days. Crew B can complete the same task in 8 days. If both crews work together, how many days will it take them to complete the task?
Assume that their work rates add linearly.
Puzzle 3: Battery Testing Strategy
You have 8 batteries, and exactly 4 of them are known to be working. A toy requires two working batteries to start. Design a strategy to find two working batteries using the minimum number of tests.
Each test involves selecting a pair of batteries and placing them in the toy. The test succeeds (the toy starts) only if both batteries in the pair are working. The goal is to find any two working batteries, not to identify all working or non-working batteries.