# probability

• Mar 27th 2007, 02:31 PM
david18
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.
• Mar 29th 2007, 06:56 AM
earboth
Quote:

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