please help...urgent!!

Hello, jai!

Quote:

A bag contains $n+7$ tennis balls:
$n$ of the balls are yellow, the other $7$ balls are white

John will take at random a ball from the bag.
He will note its colour and then put it back in the bag.

Then Mary will take at random a ball from the bag.
She will note its colour.

Given the probability than John and Mary will take balls with different colours is $\frac{4}{9}$ ,
. . prove that: . $2n^2 - 35n + 98 \:= \:0$

$\begin{array}{cc}P(\text{1st Y}) \: = \: \frac{n}{n+7} \\ P(\text{2nd W}) = \frac{7}{n+7} \end{array}\quad\Rightarrow\quad P(\text{Y, then W}) = \frac{7n}{(n+7)^2}$

$\begin{array}{cc}P(\text{1st W}) \: = \: \frac{7}{n+7} \\ P(\text{2nd Y}) = \frac{n}{n+7} \end{array}\quad\Rightarrow\quad P(\text{W, then Y}) = \frac{7n}{(n+7)^2}$

$P(\text{different colours})\:=\:\frac{7n}{(n+7)^2} + \frac{7n}{(n+7)^2} \:=\:\frac{14n}{(n+7)^2}$

We are told that this probability is $\frac{4}{9}$

Hence: . $\frac{14n}{(n+7)^2} \:=\:\frac{4}{9}\quad\Rightarrow\quad 126n\:=\:4(n+7)^2\quad\Rightarrow\quad 4n^2 - 70n + 196 \:= \:0$

Divide by 2: . $\boxed{2n^2-35n + 98 \:=\:0}$