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