Determine Probability of Single Ride on Following Day
Quick Overview
Evaluates a binomial probability setup for a ride-pricing experiment with two independent offers. Strong answers model the number of reasonable prices as Binomial(2, P), compute exactly one success as 2P(1-P), and compute permanent-rider probability as P squared.
Determine Probability of Single Ride on Following Day
Company: Lyft
Role: Data Scientist
Category: Statistics & Math
Difficulty: easy
Interview Round: Technical Screen
##### Scenario
Pricing experiment: each new rider is offered two rides on day-1; each ride price is reasonable with independent probability P.
##### Question
Calculate the probability that a rider will take exactly one ride the next day. Calculate the probability that the rider becomes a permanent rider (rides every day after the trial).
##### Hints
Model the three price-response outcomes and use probability trees or a Markov chain.
Quick Answer: Evaluates a binomial probability setup for a ride-pricing experiment with two independent offers. Strong answers model the number of reasonable prices as Binomial(2, P), compute exactly one success as 2P(1-P), and compute permanent-rider probability as P squared.
Determine Probability of Single Ride on Following Day
Lyft
Jul 12, 2025, 6:59 PM
easyData ScientistTechnical ScreenStatistics & Math
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0
Determine Probability of a Single Ride on the Following Day
A pricing experiment gives each new rider two ride opportunities on day 1. For each offered ride, the price is reasonable independently with probability P.
The rider's later behavior depends on how many reasonable prices they see on day 1:
0
reasonable prices: the rider churns.
Exactly
1
reasonable price: the rider returns the next day and takes exactly one ride.
2
reasonable prices: the rider becomes a permanent rider and rides every day after the trial.
Constraints & Assumptions
Treat the two reasonable-price events as independent Bernoulli trials with probability
P
.
Use the behavior mapping exactly as stated.
Give symbolic answers in terms of
P
.
Clarifying Questions to Ask Guidance
Are the two price offers independent?
Does "permanent rider" mean every day after the trial or just retained long term?
Are the two opportunities both on day 1, and is the next day day 2?
Part 1 - Exactly One Ride Next Day
What is the probability that the rider will take exactly one ride the next day?
What This Part Should Cover Guidance
Let the number of reasonable prices be binomial with
n = 2
and probability
P
.
Exactly one reasonable price can occur in two orders.
Final expression
2P(1-P)
.
Part 2 - Permanent Rider
What is the probability that the rider becomes a permanent rider?
What This Part Should Cover Guidance
Permanent rider corresponds to two reasonable prices.
Final expression
P^2
.
What a Strong Answer Covers Guidance
A strong answer maps the story to a binomial random variable, enumerates the two independent offers, and distinguishes exactly-one success from two successes.
Follow-up Questions Guidance
What changes if the two prices are not independent?
What value of
P
maximizes the probability of exactly one reasonable price?
What is the probability the rider returns at all after day 1?