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Math Help - probability

  1. #1
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    probability

    Hi, im trying to solve a question on a past paper; here is one that is very similar to it- New Page 1

    Im presuming the probability of blue marbles is 7/(k+7)

    On part (d) would i have to do something like:

    7/(k+7) x k/(k+7) = 4/9 ?

    Ive tried the above equation but it doesnt seem to work out seeing as it doesnt give me any square numbers as the LCM becomes 9(k+7)

    any help would be much appreciated.
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  2. #2
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    Quote Originally Posted by david18 View Post
    ...
    Im presuming the probability of blue marbles is 7/(k+7)

    On part (d) would i have to do something like:

    7/(k+7) x k/(k+7) = 4/9 ?

    ...
    Hello, david,

    you nearly did it ...

    The term
    Code:
       7       k   
    ⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯
     k + 7   k + 7
    Code:
       7       k         7k   
    ⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯ = ⎯⎯⎯⎯⎯⎯⎯⎯
     k + 7   k + 7            2 
                      (k + 7)
    describes the probability for one colour. In your problem the colour isn't mentioned so you get the same probability for the second colour too. Therefore your equation must be:

    Code:
        7k       4 
    ⎯⎯⎯⎯⎯⎯⎯⎯2 = ⎯
            2     9 
     (k + 7)
    Solve for k and you'll get:
    Code:
         7          
    k = ⎯ ∨ k = 14
         2
    These are the solutions of the equation
    Code:
    ⎛     7⎞         
    ⎜k - ⎯⎟(k - 14) = 0
    ⎝     2⎠
    Expand the brackets and multiply by 2 and you'll get the given result.

    EB
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