There are n sweets in a bag, 6 are orange, the rest yellow. Two sweets are taken out individually without replacement. The probability of which is 1/3. show n²-n-90=0

Firstly, you need to consider the type of problem we are dealing with. This is actually just a tree diagram type question. note that the sweets are not replaced.

Letting n = number of sweets in the bag. 6 are orange and n-6 are yellow. In the first selection, there are two possibilities, either yellow or orange, this is the same in the second selection. We are told that the probability of choosing two orange sweets in a row is 1/3.

From this we can set up an equation:

The probability of choosing an orange sweet on the first go is 6/n , as we have 6 orange sweets out of a total of n to pick from. This means that there are 5 orange sweets and n-1 sweets in total. 

The probability of choosing another orange sweet the second time around will be 5/(n-1). Now, in a tree diagram, when considering two selections for an overall outcome, the probabilities of the outcomes are multiplied for the final probability, as we are already given this, we can set up the quadratic equation.

6/n * 5/(n-1) = 1/3

30/(n2-n)=1/3

90=n2-n

n2-n-90=0

factorising:

(n-10)(n+9)=0

n=10, n=-9

The  number of sweets cant be negative, n>0 therefore the value for n is 10

JR
Answered by Joel R. Maths tutor

4087 Views

See similar Maths GCSE tutors

Related Maths GCSE answers

All answers ▸

How do I find the minimum turning point of a parabola?


(2x + 3y)^2 – (2x – 3y)^2 = 360 show that xy is a multiple of 5


Solve algebraically for a and b: 6a+b=16, 5a-2b=19


A stationary ball starts rolling down a hill, and after 5s it reaches a speed of 12m/s. From here the ground levels off, and the ball continues at this speed for 3 more seconds. Plot this on a velocity-time diagram.


We're here to help

contact us iconContact ustelephone icon+44 (0) 203 773 6020
Facebook logoInstagram logoLinkedIn logo

MyTutor is part of the IXL family of brands:

© 2025 by IXL Learning