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HKIMO 2020 Grade 7 National Final (Heat) Set 01 Question 22

HKIMO · HKIMO 2020 Grade 7 National Final (Heat) Set 01

Question 22

At 0:00 a box contains five black balls and one white ball. One black ball is added every 10 seconds at 0:10,0:20,0:30,…,1:00, and one white ball is added at 0:23. One ball is drawn at 0:00,0:30 and 1:00, after any black-ball addition at that time. Find the probability of drawing a white ball within the minute.

Editorial sampling assumption: each draw is uniform among balls currently in the box, and the selected ball is removed without replacement. The event is at least one white ball among the three draws.