f.5 maths probability

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:

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.

5 個解答

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  • wy
    Lv 7
    9 年 前
    最佳解答

    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.

  • 9 年 前

    欠缺JACK不溫書而考試不合格的概率

  • For Q2, I think you mean "if he does not study for the test, the probability of Jack FAILING for the test is 7/8"

    Right?

  • 9 年 前

    what do u mean?

    2011-02-05 22:18:08 補充:

    sorry I type it wrongly..sorry!

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  • 9 年 前

    If he does not study for the test, the probabily of he will pass (or fail) is what??

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