Possibility spaces Worked Solutions — GCSE Maths

Work out how many equally likely outcomes there are

The spinner has $6$ equal sections, so the sample space is the list of those $6$ equally likely outcomes. Every probability in this question is out of that total of $6$.

Find the outcomes for which the spinner lands on an even number

The favourable outcomes are 2, 4, 6. Each one is favourable because it divides exactly by $2$.

Write the probability as a fraction and simplify it

$3$ favourable outcomes out of $6$ equally likely outcomes. The highest common factor of $3$ and $6$ is $3$, so dividing top and bottom by $3$ gives $\frac{1}{2}$.

Work out how many equally likely outcomes there are

The spinner has $8$ equal sections, so the sample space is the list of those $8$ equally likely outcomes. Every probability in this question is out of that total of $8$.

Find the outcomes for which the spinner lands on a multiple of $3$

The favourable outcomes are 3, 6. Each one is favourable because it divides exactly by $3$.

Write the probability as a fraction and simplify it

$2$ favourable outcomes out of $8$ equally likely outcomes. The highest common factor of $2$ and $8$ is $2$, so dividing top and bottom by $2$ gives $\frac{1}{4}$.

Work out how many equally likely outcomes there are

The spinner has $10$ equal sections, so the sample space is the list of those $10$ equally likely outcomes. Every probability in this question is out of that total of $10$.

Find the outcomes for which the spinner lands on a number greater than $7$

The favourable outcomes are 8, 9, 10. Each one is favourable because it is bigger than $7$.

Write the probability as a fraction and simplify it

$3$ favourable outcomes out of $10$ equally likely outcomes. $3$ and $10$ share no factor bigger than $1$, so it is already in its simplest form.

Work out how many equally likely outcomes there are

The spinner has $5$ equal sections, so the sample space is the list of those $5$ equally likely outcomes. Every probability in this question is out of that total of $5$.

Find the outcomes for which the spinner lands on a prime number

The favourable outcomes are 2, 3, 5. Each one is favourable because its only factors are $1$ and itself (and it is not $1$).

Write the probability as a fraction and simplify it

$3$ favourable outcomes out of $5$ equally likely outcomes. $3$ and $5$ share no factor bigger than $1$, so it is already in its simplest form.

Work out how many equally likely outcomes there are

The spinner has $12$ equal sections, so the sample space is the list of those $12$ equally likely outcomes. Every probability in this question is out of that total of $12$.

Find the outcomes for which the spinner lands on a multiple of $4$

The favourable outcomes are 4, 8, 12. Each one is favourable because it divides exactly by $4$.

Write the probability as a fraction and simplify it

$3$ favourable outcomes out of $12$ equally likely outcomes. The highest common factor of $3$ and $12$ is $3$, so dividing top and bottom by $3$ gives $\frac{1}{4}$.