1445 views

### How do I solve Hannah’s sweet question?

This refers to a question in the Edexcel GCSE paper this year which took students to Twitter venting their frustration. The question is as follows:

‘There are n sweets in a bag. 6 of the sweets are orange. The rest of the sweets are yellow.

Hannah takes a random 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’

Seemingly out of nowhere you’re asked to prove that a certain quadratic equation holds using the information provided. The first three lines set up the situation whilst the fourth line provides you with some extra information to use to obtain the answer. Intuition should tell you that you need to calculate the probability that Hannah eats two orange sweet using the first three lines and then apply what you’re given in the fourth line.

So let’s do that. What’s the probability that the first sweet she eats from the bag is orange? There are n sweets in the bag, 6 of which are orange. So the probability is 6/n.

What’s the probability that the second sweet she eats from the bag is orange? Now there are n-1 sweets in the bag, 5 of which are orange (since she has eaten an orange sweet!). So the probability is 5/(n-1).

These two events are separate from one another, so the probability that both happen (i.e. both the sweets are orange) are the two probabilities multiplied together: 6/n × 5/(n-1) = 30/n(n-1)

But you’re told that this probability is 1/3! So all you need to do is set the expression equal to 1/3, rearrange and (hopefully!) obtain the required quadratic equation.

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

⇒ 90/n(n-1) = 1           (multiplying both sides by 3)

⇒ 90 = n(n-1)               (multiplying both sides by n(n-1))

⇒ n(n-1) – 90 = 0         (subtracting 90 from both sides)

⇒ n² – n – 90 = 0         (expanding the brackets)

Tah-dah. We’ve found the required equation and we’re done. This question was only worth three marks; a bit stingy in my opinion!

2 years ago

Answered by George, a GCSE Maths tutor with MyTutor

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

#### 780 SUBJECT SPECIALISTS

£18 /hr

Degree: Medicine (Bachelors) - Oxford, Merton College University

Subjects offered:Maths, Human Biology+ 6 more

Maths
Human Biology
Chemistry
-Personal Statements-
-Oxbridge Preparation-
-Medical School Preparation-

“I'm a second year medical student at Oxford University. Tutorials are fun, productive and tailored to you!”

£24 /hr

Degree: Dentistry (Bachelors) - Kings, London University

Subjects offered:Maths, Science+ 5 more

Maths
Science
Psychology
Chemistry
Biology
-Personal Statements-
-Medical School Preparation-

“Hi, my name is Karolina and I am a Dentistry Student from King's College London.  I understand that many students find certain aspects of the A-level syllabus challenging and having recently completed mine I believe that I know how to...”

£20 /hr

Degree: MMath Pure Mathematics (Masters) - St. Andrews University

Subjects offered:Maths, English Literature

Maths
English Literature

“I am an experienced mathematician with a personal approach to tutoring. I'm here to help you further your mathematical potential.”

£24 /hr

Degree: Mathematics (Masters) - Warwick University

Subjects offered:Maths, Further Mathematics + 1 more

Maths
Further Mathematics
.STEP.

“Premium tutor. First class graduate with teaching experience from a top Russell Group university. I deliver fun and relaxed lessons which achieve results!”

### You may also like...

#### Posts by George

Given that a and b are distinct positive numbers, find a polynomial P(x) such that the derivative of f(x) = P(x)e^(−x²) is zero for x = 0, x = ±a and x = ±b, but for no other values of x.

How do I solve Hannah’s sweet question?

Let P(z) = z⁴ + az³ + bz² + cz + d be a quartic polynomial with real coefficients. Let two of the roots of P(z) = 0 be 2 – i and -1 + 2i. Find a, b, c and d.

What values of θ between 0 and 2π satisfy the equation cosec(θ) + 5cot(θ) = 3sin(θ)?

#### Other GCSE Maths questions

What is completing the square and how do you do it?

A ladder 6·8m long is leaning against a wall. The foot of the ladder is 1·5m from the wall. Calculate the distance the ladder reaches up the wall. Give your answer to a sensible degree of accuracy.

Solve x^​2​ - 10x + 21 = 0 through the following methods: Factorisation, Completing the Square and using the Quadratic Formula

1/4 of a number is 20. What is 5 times the number?

We use cookies to improve your site experience. By continuing to use this website, we'll assume that you're OK with this.