It was a moment of head scratching, pen chewing, neck stretching, by thousands of students on June 4th 2015, when a particular tricky Maths question showed up at the exams.

Students, even maths scholars were thrown off balance all because they aimed at working out how many sweets belonged to a girl called Hannah.

Here's the question

There are n sweat in a bag,
6 of the sweets are orange
The rest of the sweets are yellow

Hannah takes at random a sweet from the bag
She eats the sweet

Hannah then takes at random another sweet from the bag
She eats the sweet

The probability that Hannah eats two orange sweets is 1/3

Show that: n2 - n- 90 =0

In Summary, the question is

Hannah has 6 orange sweets and some yellow sweets.

Overall, she has n sweets.

The probability of her taking 2 orange sweets is 1/3.

Prove that: n^2-n-90=0


Ok, here's the solution to Hannah's sweets

There are six orange sweets and n sweets overall.

If she takes one, there is a 6/n chance of getting an orange sweet.

When she takes one, there is one less orange sweet and one less sweet overall.

If she took another orange sweet, the probability would be (6-1)/(n-1)=5/n-1.

Now, you have to find the probability if she gets two orange sweets

so you simply times the two fractions: 6/n * 5/n-1 = 30/n^2-n.

It tells us the probability of two orange sweets is 1/3 which means 1/3=30/n^2-n.

We need to make the denominators the same so simply times 1/3 by 30/30 which would equal 30/90.

if 30/90 = 30/n^2-n, then n^2-n=90.

if n^2-n=90 then n^2-n-90 will equal zero.

Is that Clear?
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