Free Seat | PuzzledQuant

New on YouTube: This HRT Quant Interview Question Has a One-Line Answer - Watch now

Get quant-ready in 2026

⚡ Build the skills to land top-paying quant jobs. Offer ends in 25d 09h 51m 28s25 days 9 hours 51 minutes 28 seconds.

Easy

Probability

There are 4 people in line ahead of Bob and 3 free seats. Each of those 4 people acts independently:

with probability $2/5$ they take a seat,
with probability $1/10$ they leave the line,
with probability $1/2$ they stand (they neither take a seat nor leave).

Bob gets a free seat if at least one of the 3 seats is still free when his turn comes, i.e. if at most 2 of the 4 people ahead of him take a seat. What is the probability that Bob gets a free seat? Give an exact fraction.

Discussion (0)