請詳細解釋下條做法原因 : (唔明)
Three classes 4A, 4B and 4C attend a quiz contest. Three representatives from each class will answer 10 questions. If any representative answers a question correctly, the class will get 10 marks, otherwise they will get no marks. The probabilities that each of the 4C representatives can answer a question correctly are 0.6, 0.8 and 0.75 respectively.
a) Find the probability that the representatives of 4C will give a correct answer to a question.
我的計法 : 0.6 x 0.8 x 0.75
正確答案 : [1-[(1-0.6)x(1-0.8)x(1-0.75)]
點解要每個數各做1減, 4C答對的是0.6, 0.8, 0.75 點解不是三個相乘就是答對機會率 ?
b) Given that 4A and 4B got 80 and 60 marks respectively after answering the questions, find the probability that 4C will win the contest, correct to 4 decimal places.
完全唔識做 ?
答案 : 0.9838
急 ! F5 數 Probability 1條 5q9
2012-11-23 5:02 am
回答 (2)
2012-11-23 6:46 am
✔ 最佳答案
a)√ : one representative of 4C can answer a question correctly
X : one representative of 4C cannot answer a question correctly
P(4C gives a correct answer) + P(4C gives an incorrect answer) = 1
Hence, P(4C gives a correct answer)
= 1 - P(4C gives an incorrect answer)
= 1 - P(XXX)
= 1 - (1- 0.6) x (1 - 0.8) x (1 - 0.75)
= 0.98
Note that P(√√√) = 0.6 x 0.8 x 0.75
But P(4C gives a correct answer) = P(√√√) + P(√√X) + P(√XX) + P(√X√) + P(X√√) +P(X√X) + P(XX√)
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b)
The required probability
= P(4C answers 9 questions correctly) + P(4C answers 10 questions correctly)
= 1oC9 x (0.98)⁹ x (1 - 0.98) + (0.98)¹⁰
= 10 x (0.98)⁹ x 0.02 + (0.98)¹⁰
= 0.9838 (to 4 decimal places)
參考: 不用客氣
2012-11-23 5:11 am
a.) 題目的要求是, 只要三個representative 之中, 有一個答對就得, 所以我地先搵他們三個都答錯的可能.
P(all wrong) = 0.4*0.2*0.25 = 0.02
之後1-P(all wrong) 就得. 1-0.02
b) Not enough information wor
P(all wrong) = 0.4*0.2*0.25 = 0.02
之後1-P(all wrong) 就得. 1-0.02
b) Not enough information wor
收錄日期: 2021-04-13 19:07:43
原文連結 [永久失效]:
https://hk.answers.yahoo.com/question/index?qid=20121122000051KK00405