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HKIMO 2020 Grade 8 National Final (Heat) Set 01 Question 25

HKIMO · HKIMO 2020 Grade 8 National Final (Heat) Set 01

Question 25

A box initially contains four black balls and one white ball. One black ball is added every five seconds, at 0:05,0:10,0:15,...,1:00. One white ball is added 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 not replaced; draws occur at 0:00, 0:20, 0:40 and 1:00, including the endpoint. Each draw is uniform among the balls then present, and the target is at least one white ball.