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Math Help - Probability Question

  1. #1
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    Probability Question

    Hello, I could use some help with this one...cheers !!

    A big company produce boxes with a brand new machine that produce 10 boxes (with identical size) every minute, 7 black and the rest white (in random order). The machine pack the boxes in pairs in a special package right when it leave the production line. Let X be a random variable of the number of packages with 2 black boxes, in a minute.

    1. Build the probability function of X.
    2. Calculate the probability that out of 3 hours or producing, there will be at least
    70 minutes in which there will be found exactly 3 packages with 2 black boxes.

    thank you !
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  2. #2
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    I got a little bit of progress, maybe it will help...
    X=2,3

    P(A pair of 2 black boxes)=((3C0)*(7C2))/(10C2)=0.46666 Where C is the binomial coefficient, in the same way:
    P(A pair of 2 white boxes)=0.0666
    P(1 black and 1 white)=0.46666

    What do I do from here ?
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  3. #3
    Grand Panjandrum
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    Quote Originally Posted by WeeG View Post
    Hello, I could use some help with this one...cheers !!

    A big company produce boxes with a brand new machine that produce 10 boxes (with identical size) every minute, 7 black and the rest white (in random order). The machine pack the boxes in pairs in a special package right when it leave the production line. Let X be a random variable of the number of packages with 2 black boxes, in a minute.

    1. Build the probability function of X.
    2. Calculate the probability that out of 3 hours or producing, there will be at least
    70 minutes in which there will be found exactly 3 packages with 2 black boxes.

    thank you !
    Is that the exact wording of the problem as set? Is there any contextual background before the question?

    CB
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  4. #4
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    Yes, this is the question...I tried something else, maybe to calculate how many ways I have to set 10 boxes in a line. It didn't lead me far....
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