1. ## 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.

2. 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