MYTUTOR SUBJECT ANSWERS

569 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

328 SUBJECT SPECIALISTS

£18 /hr

Josie O.

Degree: Geography (Bachelors) - Edinburgh University

Subjects offered: Maths, Science+ 3 more

Maths
Science
Geography
Chemistry
-Personal Statements-

“About Me: Hi, I'm Josie! I'm a geography student at the University of Edinburgh; my focus is mostly on physical geography, but I also enjoy and have an interest in human geography. I'm passionate about the world around us: the process...”

£18 /hr

Maisie J.

Degree: Mathematics (G100) (Bachelors) - Warwick University

Subjects offered: Maths, Further Mathematics

Maths
Further Mathematics

“Hi! My name is Maisie and I'm studying Mathematics at Warwick University. My aim is to share my passion of maths with my students and to boost my students' self-confidence and self-esteem.  I am friendly, patient and I will adapt the ...”

MyTutor guarantee

£20 /hr

David S.

Degree: Engineering (Masters) - Warwick University

Subjects offered: Maths, Physics+ 1 more

Maths
Physics
Further Mathematics

“About MeI am a first year engineering student at the University of Warwick, I enjoy maths and physics. I am patient, reliable and flexible to suit you but the focus of my tutoring is instilling confidence into a student as they work....”

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

Make x the subject of the equation y=(2(1+x))/(3x-1)

What is 45% of 60?

How to determine the number of unique real roots of a quadratic equation.

What is the Pythagoras Equation?

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