Coin landing inside a single board square

Question

A board is tiled by squares of side $2$ inches. A coin of diameter $1$ inch is dropped so that its centre lands uniformly at random on the board. What is the chance that the coin lies entirely inside one square?

Short answer

$\tfrac14$ . By periodicity, look at one square. The coin avoids every edge exactly when its centre is at least $0.5$ inch from all four sides, i.e. in a central $1\times1$ square. The probability is $\tfrac{1}{4}$ .

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

Sample Spaces, Events, and the Probability Axioms
Conditional Probability, Total Probability, and Bayes' Rule

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

Read it free