Analyze Rider Behavior in Dynamic-Pricing Trial

Q: Analyze Rider Behavior in Dynamic-Pricing Trial

This question evaluates probability modeling skills, focusing on discrete-time stochastic processes, absorbing Markov states, independence assumptions, and conditional probability in a trial setting.

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Question

Dynamic-pricing trial: rider behavior

Context (assumptions made explicit)

Each day the rider has two potential ride opportunities.
For any specific ride opportunity, the price is "Reasonable" (R) with probability P and "High" (H) with probability 1−P, independently across rides and days.
Day 1 has already occurred with two ride opportunities; the three possible price patterns are: RR, RH/HR, HH.
While the rider is still in the trial (i.e., not yet permanent or churned), they take a ride if and only if that ride’s price is reasonable.
Absorbing behavior (implied by the hint/Markov framing):
- If on some day both prices are reasonable (RR), the rider becomes a permanent rider starting the next day (rides every day thereafter).
- If on some day both prices are high (HH), the rider churns (never rides again).
- If the day is mixed (RH or HR), the trial continues to the next day.

Questions

A) What is the probability the rider will take exactly one ride on the next day (Day 2)?

B) What is the probability the rider becomes a permanent rider (rides every day after Day 1)?

Analyze Rider Behavior in Dynamic-Pricing Trial

Dynamic-pricing trial: rider behavior

Context (assumptions made explicit)

Questions

Solution

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