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Commuter Ride-Choice Probability: Committed and Permanent Riders

LyftData Scientist · Technical Screen
MediumData ScientistTechnical ScreenStatistics & Math

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Tests discrete probability modeling, complementary counting, and Bayesian updating to analyze multi-day commuter behavior across distinct rider segments.

Scenario

Lyft is analyzing weekday commute patterns to design targeted commuter passes. Marketplace analysts classify new commuters into two latent segments upon onboarding:

  • Committed Riders (C): Represent 25% of the population (P(C) = 0.25). On any given weekday, a Committed Rider books a morning commute ride with probability P(Ride | C) = 0.80.
  • Flexible Riders (F): Represent 75% of the population (P(F) = 0.75). On any given weekday, a Flexible Rider books a morning commute ride with probability P(Ride | F) = 0.20.

Assume that, conditional on a rider's segment, daily ride choices are independent and identically distributed across weekdays.

Questions

  1. Weekly Activation Probability: What is the probability that a randomly chosen new commuter takes at least one morning commute ride during a standard 5-day workweek (Monday through Friday)? Express your answer as an exact decimal or simplified fraction.

  2. Segment Inference via Bayes' Theorem: An unidentified new commuter is observed over their first 3 weekdays and takes a Lyft ride on all 3 days. Given this observation, what is the posterior probability that this commuter is a Committed Rider?

  3. Next-Day Forecasting: Given that the commuter in Question 2 took a ride on each of their first 3 weekdays, what is the probability that they will also take a ride on Day 4?

Assumptions & Expectations

  • State formulas clearly using standard probability notation before substituting numbers.
  • Clearly show intermediate steps (e.g., likelihoods, marginal probabilities, and posterior calculations).

Hints

Hint 1

To find the probability of at least one ride over 5 days, use the complement rule within each segment before applying the Law of Total Probability.

Hint 2

For the posterior segment probability, compute the joint probability of 3 consecutive rides for each rider type, then normalize by the total probability of 3 consecutive rides.

Hint 3

For Day 4 prediction, condition on the updated posterior segment probabilities rather than the unconditioned prior.

Follow-up questions

  • How would you handle day-to-day correlation where taking a ride on day t increases the likelihood of taking a ride on day t+1 (e.g., Markov transition model)?
  • How would you estimate the rider segment mixture proportions and ride probabilities from unlabelled historical trip logs?
  • If a rider's daily choice probability is continuous rather than binary (e.g., Beta-distributed across users), how does the posterior update change?