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There are n types of coupons. We collect coupons one-by-one. Each coupon collected is of type...

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Advance Math

There are n types of coupons. We collect coupons one-by-one.Each coupon collected is of type i with probability pi P , andindependent of other coupons. Assume that n i=1 pi = 1. Suppose intotal k coupons are collected. Define Ai to be the event that thereis at least one type i coupon among those collected for i = 1, 2, ·· · , n.

(a) Compute P(Ai)

(b) For any i 6= j, find P(Ai ? Aj )

(c) Compute P(Ai |Aj ), hint: use formula about P(A ? B) = . ..

Answer & Explanation Solved by verified expert
4.3 Ratings (715 Votes)
a Since Ai is the event that there is atleast onetype i coupon among those collected henceAic is the event that there is notype i coupon among those collectedThe probability that the first coupon collected is not of type i is1piThe probability that the second coupon collected is not of type iis 1piThe probability    See Answer
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