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2 problems match “coupon collector problem”. Clear

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1. Draws to see all six unique balls ●●●○○ 50 ptsA jar contains 66 white balls and 6 unique balls: 1 red, 1 blue, 1 green, 1 purple, 1 yellow and 1 cyan. Balls are drawn one at a time, each ball is returned to the jar after it is drawn, and the colours are recorded. What is the expected number of draws needed until all 6 uniquely coloured balls have been seen at least once?
2. Minimum people covering every birthday ●●●●○ 100 ptsAssume a year has 365 equally likely birthdays, each person's birthday is independent of the others, and leap years are ignored. What is the minimum number of people needed so that the probability that every one of the 365 days is someone's birthday is greater than $0.5$?