Problem in Probability

久-狗

2012-10-03 7:38 am

Please help to answer the following question.

Question
To redeem a souvenir from a chain store, one must collect a set of frou different types of coupons, namely A, B, C, D. Suppose that a customer has collected 10 coupons independently, wtih each equally likely to be one of these four 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 8:47 am

✔ 最佳答案

(a)
P(no A in 10 coupons)
= P(all 10 coupons are B, C or D)
= (3/4)¹⁰
= 59049/1048576

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(b)
P(no A and B in 10 cards)
= P(all 10 coupons are C or D)
= (2/4)¹⁰
= (1/2)¹⁰
= 1/1024

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(c)
P(cannot redeem a souvenir)
= P([no A in 10 coupons] or [no B in 10 coupons] or [no C in 10 coupons] or [noA in 10 coupons])
= 4 x (3/4)¹⁰
= 3¹⁰/4⁹
= 59049/262144

P(can redeem a souvenir)
= 1 - P(cannot redeem a souvenir)
= 1 - (59049/262144)
= 203095/262144

參考: micatkie

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