I'm collecting toys, they come in blind packs and there are 9 of them. Therefore for the first toy I have a 1.0 probability of getting a toy I haven't had before, then a 8/9, then a 7/9 and so on. On average, how many toys will I need to buy before I get the whole set?
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This is known as the Coupon Collector Problem – lulu Mar 20 '17 at 14:00
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Also see this question and others on the site under coupon collector. – Ross Millikan Mar 20 '17 at 14:04