MATHS M1 - Ans.fyi 參考答案

MATHS M1

2012-06-30 8:43 pm

it is known that 2% of the batteries produced by a certain factory are defective .the factory sells batteries in packages of 10 and offers a replacement if more than 1 of the 10 batteries is defective.

(a) what proportion of packages sold must the factory replace ?

(b) if Sam buys 10 packages, find the probability that 3 of them need to be replaced

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回答 (1)

胡雪8°

2012-06-30 11:45 pm

✔ 最佳答案

已知某廠所生產的電池中有 2% 是損壞的。該廠以十枚電池包裝出售，並承諾十枚電池中多於一枚電池損壞就會退換。
(a) 該廠必定要退換的售出電池包裝所佔的比例是多少？
(b) Sam 買了 10 包電池，計算其中 3 包需要更換的概率。

(a)
P(No battery is defective out of the 10 batteries)
= (1 - 2%)^10
= 0.98^10

P(1 battery is defective out of the 10 batteries)
= C(10,1) x (2%) x (1 - 2%)^9
= 0.2 x 0.98^9

P(more than 1 battery is defective out of the 10 batteries)
= 1 - (0.98^10 + 0.2 x 0.98^9)
= 0.01618 (to 4 sig. fig.)

Proportion of packages sold that the factory must replace
= 0.01618
= 1.618%

=====
(b)
P(out of 10 packages, 3 of them need to be replaced)
= C(10,3) x (0.01618)^3 x (1 - 0.01618)^7
= (10!/3!7!) x (0.01618)^3 x (1 - 0.01618)^7
= 0.0004534 (to 4 sig. fig.)

參考: 胡雪

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