Finishing a slice in the next minute

Question

The time needed to eat one slice of pizza is uniform between $1$ and $5$ minutes. Someone has already been eating a slice for $2$ minutes and is not finished. What is the probability they finish within the next minute?

Short answer

$\tfrac13$ . Conditioning a uniform time on having already passed 2 minutes leaves it uniform on the remaining window $[2,5]$ , which is 3 minutes long. Finishing by minute 3 covers 1 minute of that window, so the probability is $\tfrac13$ .

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

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Lessons behind this question

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

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