Lyft·Data Scientist·Technical Phone Screen
- A commuter takes two trips per day (morning and evening) with independent probabilities p and 2p of using the ride-hailing service. What is the probability the commuter takes at least one ride on a given day?
- What is the probability that a commuter takes both the morning and evening rides on the same day, making them a 'committed' rider?
- A rider uses the service on Day 1. What is the probability they take at least one ride again on Day 2, given that days are independent and follow the same model?
- What is the probability that a new rider becomes a 'permanent' rider within two days, defined as being a committed rider (both trips) on at least one of Day 1 or Day 2?
- Given that a rider took at least one ride on Day 2, what is the probability they took no evening (high-priced) ride on Day 1?
- How would the answers change if morning and evening trip decisions within a day were positively correlated rather than independent?
- Across N independent commuters, what is the distribution of the number who become committed riders on a given day? What are its mean and variance?
- If you observed the empirical fraction of committed riders in real data, how would you estimate p and construct a confidence interval around it?
“Complement is the move here, 1 minus the probability of skipping both trips.”