Compute Commuter Ride Probabilities
Company: Lyft
Role: Data Scientist
Category: Statistics & Math
Difficulty: medium
Interview Round: Technical Screen
A commuter takes two trips per day: one morning commute to work and one evening commute home.
Let `M` be the event that the commuter uses Lyft for the morning trip, and let `E` be the event that the commuter uses Lyft for the evening trip.
You are given:
- `P(M) = p`, where `p < 1/3`.
- If the commuter uses Lyft in the morning, then the probability they use Lyft in the evening is `P(E | M) = 2p`.
- If the commuter does not use Lyft in the morning, then the probability they use Lyft in the evening is `P(E | not M) = p`.
Answer the following:
1. What is `P(E)`, the probability the commuter uses Lyft for the evening trip?
2. What is the expected number of Lyft trips the commuter takes per day?
3. What is `P(M | E)`, the probability the commuter used Lyft in the morning given that they used Lyft in the evening?
Quick Answer: This question evaluates proficiency with conditional probability, Bayes' theorem, and expected value by requiring manipulation of joint, marginal, and posterior probabilities.