f.5 maths probability

👨🏻‍🏫 學術台數學

[匿名]

2011-02-06 4:34 am

1. In secondary school, the ratio of the no.of boys to girls is 3:2. 10% of the boys and 1% of the girls are members of the mathematics club. What is the probability that a student chosen at random is a member of the mathematics club? (give your answer in decimal)

2. If Jack studies for tomorrow's test, the probabilty that he will pass the test is 4/5; if he does not study for the test, the probabily of Jack studying for the test is 7/8, find the probability that he will fail the test.

更新1:

2.If Jack studies for tomorrow's test, the probabilty that he will pass the test is 4/5; if he does not study for the test, the probabily of Jack will pass the test is 1/10, Given that the probability of Jack studying for the test is 7/8, find the probability that he will fail the test.

回答 (5)

用戶10012

2011-02-06 6:36 am

✔ 最佳答案

1. P(Boy) = P(B) = 3/5 = 0.6. P(Girl) = P(B') = 1 - 3/5 = 2/5 = 0.4.
P(Member given that the student is a boy) = P(M|B) = 10% = 0.1
P(Member given that the student is a girl) = P(M|B') = 1% = 0.01
By Law of Total Probability,
P(Member of Maths Club) = P(M) = P(M|B)P(B) + P(M|B')P(B')
= 0.1 x 0.6+ 0.01 x 0.4 = 0.06 + 0.004 = 0.064.
2.
P(Pass the test given that Jack study) = P(A|S) = 4/5 = 0.8
P(Pass the test given that Jack does not study) = P(A|S') = 1/10 = 0.1
P(Jack studies) = P(S) = 7/8 = 0.875, so P(S') = 1 - 0.875 = 0.125
Again by Law of Total probability,
P(Fail the test) = P(A') = P(A'|S)P(S) + P(A'|S')P(S')
= (1 - 0.8) x 0.875 + (1 - 0.1) x 0.125
= 0.175 + 0.1125 = 0.2875.

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myisland8132

2011-02-06 6:16 am

欠缺JACK不溫書而考試不合格的概率

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