Odds the fourth weekday of a month is Thursday

Question

Business days are Monday to Friday (ignore public holidays), and a month is equally likely to begin on any day of the week. What is the probability that the month's fourth business day is a Thursday?

Short answer

$3/7$ . Check each starting day: a month starting on Saturday, Sunday or Monday has business days Mon, Tue, Wed, Thu first, so the fourth is Thursday; starting Tuesday through Friday pushes it to another day. That is $3$ of $7$ cases.

Adapted from Joshi, Denson & Downes, Quant Job Interview Questions and Answers, Q3.16, p.82; question and answer rewritten by SelfMadeQuant.com.

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Lessons behind this question

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

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