Determine Probability of Single Ride on Following Day

Q: Determine Probability of Single Ride on Following Day

This question evaluates a candidate's understanding of basic probability and binomial/Bernoulli reasoning for independent events in the Statistics & Math domain.

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Question

Trial Pricing Experiment with Two Offers

Setup

A new rider is given a trial on day 1 with two ride opportunities. For each offered ride, the price is "reasonable" independently with probability P.

Assume the rider's behavior is driven by how many reasonable prices they see on day 1:

0 reasonable prices → the rider churns (does not return).
Exactly 1 reasonable price → the rider returns the next day and takes exactly one ride.
2 reasonable prices → the rider is delighted and becomes a permanent rider (rides every day after the trial).

Questions

What is the probability that the rider will take exactly one ride the next day?
What is the probability that the rider becomes a permanent rider (rides every day after the trial)?

Determine Probability of Single Ride on Following Day

Trial Pricing Experiment with Two Offers

Setup

Questions

Solution

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