Square numbers probability help

[david18]

Hi, I am trying to solve a question on a past paper; here is one that is very similar to it- http://www.gcsemathspastpapers.com/images/p5j04q19.htm

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 doesn't seem to work out seeing as it doesn't give me any square numbers as the LCM becomes 9(k+7)

any help would be much appreciated.

 

[drpizza]

You're correct for the probability of blue.

For the second part, you're really close. You have the probability that the first girl gets blue and the 2nd girl gets red. Isn't there something else that could happen such that they still have different colors? (Then, simplify and cross multiply)

edit:
You have $$\frac{7}{k+7}*\frac{k}{k+7} = \frac{4}{9}$$

= $$\frac{7k}{(k+7)^2}=\frac{4}{9}$$

Are you sure you don't end up with a $$k^2$$ term in there?