Thread: 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.

Originally Posted by david18

...
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         7·k   
⎯⎯⎯⎯⎯·⎯⎯⎯⎯⎯ = ⎯⎯⎯⎯⎯⎯⎯⎯
 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:

    7·k       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