MYTUTOR SUBJECT ANSWERS

476 views

Show that n^2 -n - 90 = 0

This is the full question:

There are n sweets in a bag. 6 sweets are orange. The rest of the sweets are yellow. Hannah takes a sweet out of the bag at random. She eats the sweet and then takes another at random. She eats the second sweet.  The probability that Hannah eats two orange sweets is 1/3. Show that n2 - n - 90 = 0

This is the question that caused much upset and pain during this years GCSE exam. But hopefully with my explanation we can work out what is going on.

Always in wordy question extract your information:

- n sweets (n could be any number)

- 6 orange 

- picks 2 sweet one at a time and eats them

The fact that she eats them is important because in probability we call this non-replacement (she is not putting the sweets back in so the probability of picking an orange/yellow sweet is always changing). 

- probability of orange and orange again is 1/3

So because we are not replacing the sweets we know that to get 2 orange, she picks an orange first and then another. 

If there are 6 to start of with, the chance of me picking one is 6/n. (n is the total number of sweets)

I eat this sweet so there is one less sweet in the bag: n-1 (n was the original total, now there is one less)

Therefore the probability of me taking another orange providing I have already picked one is  5/n-1

We were told in the question the probability of picking 2 orange is 1/3.

So:

6/n x 5/n-1 = 1/3

We know that when we multiply factions - you can do so instantly - no need to change anything so you get:

30/n(n-1) = 1/3

Lets multiply both sides by 3

90/n(n-1) = 1

Now lets multiply both sides by n(n-1)

90 = n(n-1)

Expand the brackets

90 = n- n 

Subtract 90 on both sides

n2 - n - 90 = 0

You have solved the questions and shown full working.

Dylan N. GCSE Maths tutor, GCSE Law tutor, Mentoring -Personal Statem...

1 year ago

Answered by Dylan, a GCSE Maths tutor with MyTutor

Still stuck? Get one-to-one help from a personally interviewed subject specialist

327 SUBJECT SPECIALISTS

£18 /hr

Fabiha A.

Degree: Biomedical Science (Bachelors) - Kings, London University

Subjects offered: Maths, Science+ 2 more

Maths
Science
Chemistry
Biology

“About me I am currently studying Biomedical Science at King's College London because it combines my twomost loved subjects, Biology and Chemistry. My enthusiasm for all things science make me want to keep learning and also use my kno...”

£22 /hr

Dorian A.

Degree: Theoretical Physics (Masters) - Durham University

Subjects offered: Maths, Physics+ 1 more

Maths
Physics
Further Mathematics

“About Me As a Theoretical Physics student at Durham University, I am more than aware of all of the confusing turns that science can take. I have areal passion for my subject, and hope to show my students howbeautiful science can be.  ...”

£20 /hr

Daniel S.

Degree: Philosophy, Politics and Economics (Bachelors) - Oxford, Christ Church University

Subjects offered: Maths, History+ 5 more

Maths
History
Extended Project Qualification
Economics
.TSA. Oxford.
-Personal Statements-
-Oxbridge Preparation-

“I am a Philosophy, Politics and Economics student at the University of Oxford. I am a very versatile tutor, with my degree affording me the skills to aid students with both scientific problems, as well as being able to help those with...”

MyTutor guarantee

About the author

Dylan N.

Currently unavailable: for regular students

Degree: Law (Bachelors) - Oxford, St Catherine's College University

Subjects offered: Maths, Law+ 2 more

Maths
Law
Economics
-Personal Statements-

“I am a law student at Oxford University and looking forward to working with you. I have done a vast amount of mentoring whilst at school so I am extremely friendly and approachable. Questions are the best way to learn so never be afra...”

MyTutor guarantee

You may also like...

Other GCSE Maths questions

What is 45% of 60?

How do I complete the square of an equation?

How to solve a simple simultaneous equation

Rearranging formulae

View GCSE Maths tutors

Cookies:

We use cookies to improve our service. By continuing to use this website, we'll assume that you're OK with this. Dismiss

mtw:mercury1:status:ok