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Math Help - Spot my mistake please...

  1. #1
    Junior Member
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    Spot my mistake please...

    In a class of 30 students,10 of them come to school by bus,12 students walk to school and the others by car. 6 students are randomly selected. Find the probability that

    (a) only 1 student come to school by car (ans:0.3548)

    (b) at least 2 students come to school by bus (ans: 0.6736)

    (c) equal number of students from each category is selected. (ans: 0.1401)

    My attempt:

    (a) Probability that a student comes to school by car is 8/30=4/15

    X~B(6,4/15)

    P(X=1) = 6C1 x (4/15) x (11/15)^5
    = 0.3393

    (b) Probability that a student comes to school by bus is 10/30 = 1/3

    Y~B(6,1/3)

    P(Y=>2) = 1- 6C1 x (1/3) x (2/3)^5 - 6C0 x (1/3)^0 x (2/3)^6
    = 0.6488

    (c) Probability that a student comes to school on foot is 12/30=2/5

    F~B(6,2/5)

    P(2F,2Y,2X) = 6C2 x (2/5)^2 x (3/5)^4 x 4C2 x (1/5)^2 x (2/5)^2 x 1
    = 0.01194

    What is the mistake in my approach?
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  2. #2
    Grand Panjandrum
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    Quote Originally Posted by cyt91 View Post
    In a class of 30 students,10 of them come to school by bus,12 students walk to school and the others by car. 6 students are randomly selected. Find the probability that

    (a) only 1 student come to school by car (ans:0.3548)
    My attempt:

    (a) Probability that a student comes to school by car is 8/30=4/15

    X~B(6,4/15)
    No the number that come by car does not have a binomial distribtion.

    The probability that the first student came by car is 8/30, then that the next did not come by car is 22/29, and then next 21/28, ...

    So the required probbailty that the first came by car and the rest did not is:

    (8x22x21xx20x19x18)/(30x29x29x27x26x27).

    The total probabilty you require is six times this (to account for the cases where the child coming by car is the 1st, 2nd, ..., 6th).

    CB
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  3. #3
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    Ok. Thanks a lot. Is it correct to say that binomial distribution is used if the probability is constant for all trials?
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  4. #4
    MHF Contributor Unknown008's Avatar
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    Well, the binomial distribution is used only when the probability is constant throughout all trials

    (with some other conditions as well)
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  5. #5
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    Thanks. You guys have been helpful.
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