Two uniform points on an interval straddling zero

Question

Two numbers are drawn independently and uniformly from the interval $(-1,2)$ . What is the probability that $0$ lies between them?

Short answer

$\tfrac49$ . Each point is negative with probability $\tfrac13$ and positive with probability $\tfrac23$ . Zero separates them when their signs differ: $2\cdot\tfrac13\cdot\tfrac23=\tfrac49$ .

Adapted from QuantQuestions.io; question and answer rewritten by SelfMadeQuant.com.

See the hint and the full worked solution in the question bank (free account).

Open the worked solution

Lessons behind this question

Continuous Random Variables and Probability Density Functions
Cumulative Distribution Functions
Sample Spaces, Events, and the Probability Axioms

Start with a free lesson: Normal Distribution is part of a free topic. Create a free account, no card needed, to read it in full with worked solutions.

Read it free