F5 maths help plz

2013-10-02 1:41 am

1. 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.
(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.

回答 (1)

50418129

2013-10-02 4:43 pm

✔ 最佳答案

(a)

P(get a correct answer)
= P(at lease one representive get a correct answer)
= 1 - P(no representive get a correct answer)
= 1 - (1 - 0.6)(1 - 0.8)(1 - 0.75)
= 0.98

(b)

P(win the contest)
= P(get 100 marks or 90 marks)

= (0.98)(0.98)(0.98)(0.98)(0.98)(0.98)(0.98)(0.98)(0.98)(0.98)
+ (0.98)(0.98)(0.98)(0.98)(0.98)(0.98)(0.98)(0.98)(0.98)(0.02)
+ (0.98)(0.98)(0.98)(0.98)(0.98)(0.98)(0.98)(0.98)(0.02)(0.98)
+ (0.98)(0.98)(0.98)(0.98)(0.98)(0.98)(0.98)(0.02)(0.98)(0.98)
+ (0.98)(0.98)(0.98)(0.98)(0.98)(0.98)(0.02)(0.98)(0.98)(0.98)
+ (0.98)(0.98)(0.98)(0.98)(0.98)(0.02)(0.98)(0.98)(0.98)(0.98)
+ (0.98)(0.98)(0.98)(0.98)(0.02)(0.98)(0.98)(0.98)(0.98)(0.98)
+ (0.98)(0.98)(0.98)(0.02)(0.98)(0.98)(0.98)(0.98)(0.98)(0.98)
+ (0.98)(0.98)(0.02)(0.98)(0.98)(0.98)(0.98)(0.98)(0.98)(0.98)
+ (0.98)(0.02)(0.98)(0.98)(0.98)(0.98)(0.98)(0.98)(0.98)(0.98)
+ (0.02)(0.98)(0.98)(0.98)(0.98)(0.98)(0.98)(0.98)(0.98)(0.98)

= (0.98)^10 + (10C1) (0.98)^9 (0.02)
= 0.9838

參考: knowledge

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