Probabiliy,coupons collection

Lok

2012-09-30 3:30 am

To redeem a souvenir from a chain store, one must collect a set of five different types of coupons, namely A, B, C, D, E Suppose that a customer has collected 12 coupons independently, with each equally likely to be one of these five types.
(a) Find the probability that the customer has no coupon of type A.
(b) Find the probability that the customer has no coupon of type A and type B.
(c) Find the probability that the customer can redeem a souvenir.

回答 (1)

micatkie

2012-10-03 9:29 am

✔ 最佳答案

(a)
P(no A in 12 coupons)
= P(all 12 coupons are B, C, D and E)
= (4/5)^12
= 16777216/244140625

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(b)
P(no A and B in 12 coupons)
= P(all 12 coupons are C, D and E)
= (3/5)^12
= 531441/244140625

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(c)
P(cannot redeem a souvenir)
= P([no A in 12 coupons] or [no B in 12 coupons] or [no C in 12 coupons] or [noD in 12 coupons] or [no E in 12 coupons])
= 5 x (16777216/244140625)
= 16777216/48828125

P(can redeem a souvenir)
= 1 - P(cannot redeem a souvenir)
= 1 - (16777216/48828125)
= 32050909/48828125

參考: micatkie

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