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HKIMO 2019 Grade 8 National Final (Heat) Set 02 Question 25

HKIMO · HKIMO 2019 Grade 8 National Final (Heat) Set 02

Question 25

A box initially contains seven black balls and one white ball. Add a black ball every five seconds at 0:05, 0:10,..., 1:00, and add a white ball at 0:29. Starting at 0:00, draw one ball every 20 seconds, after any addition at that time. Find the probability of drawing a white ball within one minute.

Editorial interpretation: drawn balls are removed, not replaced. Draw uniformly at 0:00, 0:20, 0:40 and 1:00, including the endpoint. The target is at least one white ball.