probability questions (ce 程度)

2009-08-30 2:55 am

請詳細列明算式、步驟(最好有解釋)thanks

1. The three classes 5A,5B and 5C attend a quiz contest. Three representatives from each class will answer 10 questions, and every question has to be answered. If any representative answers a question
correctly, the class will get 10 marks, otherwise they will get no mark. The probabilities that each of the 5C representatives can answer a question correctly are 0.6, 0.8 and 0.75 respectively. Given that 5A and 5B got 80 and 60 marks respectively, find the probability that 5C will win the contest.
2.In a game, two players A and B take turns to throw a dice. The one who gets a 6 first wins the game. If A starts the game, find the probability of each of
(a)A wins the game
(b)B wins the game

回答 (1)

myisland8132

2009-08-30 3:28 am

✔ 最佳答案

1

The probabilities that each of the 5C representatives can answer a question correctly are 0.6, 0.8 and 0.75
So
The probabilities that each of the 5C representatives can not answer a question correctly are 0.4, 0.2 and 0.25
The probabilities that all of the 5C representatives can not answer a question correctly is 0.4(0.2)(0.25)=0.02
The probabilities that at least one of the 5C representatives can answer a question correctly is 1-0.02=0.98
IF 5C will win the contest, then 5C needs answer 10 questions and 9 or 10 questions is corrected
P=10(0.98)^9(0.02)+0.98^10=0.9838
the probability that 5C will win the contest
=0.9838
2(a)
P(A wins the game)
=1/6+(5/6)(5/6)(1/6)+(5/6)(5/6)(5/6)(5/6)(1/6)...
=(1/6)[1+(5/6)^2+(5/6)^4+...]
=(1/6){1/(1-25/36)]
=(1/6)(36/11)
=36/66
=6/11
(b) P(B wins the game) = 1-6/11=5/11

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