Calculate conditional probability for click-through rates

Last updated: June 4, 2026

Quick Overview

Given the following scenario about revenue per session, calculate the the p-value.

Expedia

Statistics & Math

Data Scientist

Expedia

June 4, 2026

Data Scientist

Technical Screen

Statistics & Math

Hard

4,320 solved

Given the following scenario about revenue per session, calculate the the p-value.

This statistics question from Expedia's Technical Screen tests your ability to apply mathematical reasoning to practical problems. The interviewer expects precise definitions, correct methodology, and awareness of assumptions and limitations.

What the Interviewer Expects

Derive results from first principles when needed
Handle complex scenarios with multiple interacting variables
Design experiments that account for real-world complications
Discuss advanced topics: Bayesian methods, causal inference, resampling
Connect statistical concepts to business decision-making
Identify subtle errors in reasoning (Simpson's paradox, survivorship bias)

Key Topics to Cover

Bayesian vs frequentist inference

Power analysis and sample size calculation

Causal inference basics

Conditional probability and Bayes theorem

How to Approach This

Define your hypotheses (H0 and H1) clearly before performing any test.
Calculate required sample size BEFORE running an experiment, using power analysis.
Remember the Central Limit Theorem: sample means become approximately normal with large n.
Watch for Simpson's paradox. Always segment data by key dimensions.
Distinguish between statistical significance and practical significance.

Possible Follow-up Questions

What assumptions does this test make, and how would you validate them?
What if the sample size is very small?
How would you design a follow-up experiment based on these results?

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Sample Answer

Problem Formulation

In this problem, we need to calculate the conditional probability of the click-through rate (CTR) given the revenue per session for Expedia's users. Let's denote:

$A$ : the event that a user cli...

Solution Approach

Calculate $P(A)$ : This is the overall click-through rate. For instance, if we have data showing that 15% of users click on ads, then $P(A) = 0.15$ .
Calculate $P(B | A)$ : Thi...

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