#### bumblebee123

##### New member

- Joined
- Jan 3, 2018

- Messages
- 20

A bag contains (n+7) balls. n are the number of yellow balls.The other 7 balls are white.

I already have the expression, in terms of n, for the probability of taking a white ball:

7/n+7

I am now told.

There are two people. After John has put the ball back into the ball bag, Mary takes a ball at random from the bag. Given the probability that John and Mary will take balls of different colours is 4/9 prove that 2n^2 - 35n + 98 = 0

So far I have done this:

If they both choose a ball each and the ball are different colours then I need to use the formula for a ball being white and another being yellow and as they are independent probabilities I will need to multiply them, I have done this:

n/n+7 x 7/n+7 = 4/9

I try to get the equation to resemble the 2n^2 - 35n + 98 = 0 and proceed to :

7n/(n+7)^2= 4/9

7n = 4/9 (n+7)^2

63n = 4 (n+7)^2

63n = 4 (n^2 + 14n +49)

63n = 4n^2 + 56n + 196

0 = 4n^2 -7n +196

I see that if I divide my 2 as a common factor I get:

0 = 2x^2 -3.5n - 98

Which is nearly what I need but the coefficient for n is not right.

Please can you help? I don't know where I have gone wrong or if this is a misprint in the book - maybe.

Thank you.