← Mistral AI Interview Insights
My first instinct was to just halve 0.99, which is obviously wrong but the brain does weird things under pressure.
Model car arrivals as a Poisson process, where the probability of at least one event in time t is 1 - e^{-λt}. Use the given probability for t=1 hour to solve for λ, then compute the probability for t=0.5 hours.
Pro tip: State the Poisson assumption explicitly and note that it implies independent arrivals with a constant rate. This shows you understand the underlying model and avoids ambiguity.
Recognize that car arrivals can be modeled as a Poisson process, where the number of events in a fixed interval follows a Poisson distribution.
Use the formula P(at least one in t) = 1 - e^{-λt}. Plug in the given probability for t=1 hour: 0.99 = 1 - e^{-λ}.
Rearrange to find e^{-λ} = 0.01, then take the natural logarithm: λ = -ln(0.01) ≈ 4.605 events per hour.
For t=0.5 hours, compute P(at least one) = 1 - e^{-λ*0.5} = 1 - e^{-2.3025} ≈ 1 - 0.1 = 0.9.
Check that the result is less than 0.99 and greater than 0, which makes sense. Present the answer clearly with the assumption stated.
AI-generated suggestions, not part of the candidate's original notes. May be inaccurate — verify before relying on them.
Treat the problem as a rates problem: find each crew's work rate (jobs per day), add them to get the combined rate, then take the reciprocal to find the time. State the formula clearly and compute the answer as 24/7 days (about 3.43 days).
Pro tip: Mention that this is a harmonic mean problem and that the result is always less than the fastest individual time, which shows deeper understanding. Also, if coding, note that using floating-point division is fine but be aware of precision issues in real systems.
Express each crew's rate as jobs per day: Crew A does 1/6 job per day, Crew B does 1/8 job per day.
Add the rates to get the combined rate: 1/6 + 1/8 = 7/24 job per day.
Take the reciprocal of the combined rate to find the time: 24/7 days, which is approximately 3.43 days.
Verify that the answer is less than the faster crew's time (6 days) and explain why this makes sense.
AI-generated suggestions, not part of the candidate's original notes. May be inaccurate — verify before relying on them.
This one took me a while and I think I overcomplicated it initially by trying to think about it like a sorting problem.
Model the problem as finding a pair of working batteries among 8 with exactly 4 working. Use a combinatorial strategy: test pairs of batteries in a way that maximizes information gain, such as partitioning into groups and testing within groups, to guarantee finding a working pair in the minimum number of tests.
Pro tip: Demonstrate that you understand the worst-case guarantee by considering adversarial placement of working batteries. Mention that the answer is 7 tests, and explain why fewer cannot guarantee success.
Clarify that there are exactly 4 working and 4 non-working batteries, and a test consists of inserting two batteries into the toy and observing if it turns on. The goal is to guarantee finding a working pair in the minimum number of tests.
Argue that with fewer than 7 tests, an adversary could arrange the working batteries to avoid detection. For example, after 6 tests, there could still be a configuration where no tested pair works.
Partition the 8 batteries into two groups of 4. Test all pairs within the first group (6 tests). If none work, then the first group has at most 1 working battery, so the second group has at least 3 working batteries. Then test any pair from the second group (1 test) to find a working pair.
Show that if a working pair is found in the first group, we are done. If not, the second group must contain at least 3 working batteries, so any pair from it will work, guaranteeing success in 7 tests.
Explain that 7 is minimal because with 6 tests, an adversary could place the 4 working batteries such that no tested pair works (e.g., at most one working battery in each tested pair).
AI-generated suggestions, not part of the candidate's original notes. May be inaccurate — verify before relying on them.