this question is contained on a gcse past paper i am doing and i think im approaching it from the wrong angle but have tried a few times and dunno where i am going wrong :( hope you can help(adsbygoogle = window.adsbygoogle || []).push({});

1. The problem statement, all variables and given/known data

A bag contains (n+7) tennis balls.

nof the balls are yellow.

The other 7 balls are white.

John will take at random a ball from the bag.

He will look at its colour and then put it back in the bag.

part a)Bill states that the probability that John will take a white ball is 2/5

Prove that Bill's statement cannot be correct.

part b)After John has put the ball back into the bag, Mary will then take at random a ball from the bag.

She will note its colour.

Given the probability that John and Mary will take balls with different colours is 4/9, prove that 2n^2 - 35n + 98 = 0

2. Relevant equations

3. The attempt at a solution

a)(I think I got this bit right)

2/5 = 7/(n+7)

n+7 = 7/(2/5)

n+7 = 7/0.4

n+7 = 17.5

n = 10.5

Bill's statement cannot be write because there cannot be a non-interger number of balls.

b)

I did a probability tree thing and worked out there are 2 ways that they will have different colours, each with a 7n/(n+7) probability.

therefore, there is a 14n/(n+7) chance of them selecting different colours.

(this is where i might be going wrong)

so, 14n/(n+7) = 4/9

126n/(n+7) = 4

n+7 = 126n / 4

n+7 = 31.5n

7 = 30.5n

??

this is where i get stuck cause i realise i shouldnt being working out n should I?

is it i have to factorise it out somewhere? get it in quadradic form or whatever?

hope you can help

thnx

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# Probability color ball problem

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