Expected outcomes Worked Solutions — GCSE Maths

Check that the outcomes are equally likely

The question says the spinner is fair, so each of the $8$ sections is equally likely. That is what makes it safe to work the probability out by counting outcomes.

Write down the probability

For equally likely outcomes the probability is the number of favourable outcomes over the total: $\frac{3}{8}$. $3$ and $8$ have no common factor bigger than $1$, so it is already in its simplest form. The favourable outcomes are the $3$ red sections.

State the answer

So the probability that the spinner lands on red is $\frac{3}{8}$.

Check that the outcomes are equally likely

The question says the spinner is fair, so each of the $10$ sections is equally likely. That is what makes it safe to work the probability out by counting outcomes.

Write down the probability and simplify it

For equally likely outcomes the probability is the number of favourable outcomes over the total: $\frac{4}{10}$. The highest common factor of $4$ and $10$ is $2$, so this simplifies to $\frac{2}{5}$. The favourable outcomes are the $4$ red sections.

State the answer

So the probability that the spinner lands on red is $\frac{2}{5}$.

Check that the outcomes are equally likely

The question says the spinner is fair, so each of the $12$ sections is equally likely. That is what makes it safe to work the probability out by counting outcomes.

Write down the probability and simplify it

For equally likely outcomes the probability is the number of favourable outcomes over the total: $\frac{4}{12}$. The highest common factor of $4$ and $12$ is $4$, so this simplifies to $\frac{1}{3}$. The favourable outcomes are the $4$ green sections.

State the answer

So the probability that the spinner lands on green is $\frac{1}{3}$.

Check that the outcomes are equally likely

The question says the counter is fair, so each of the $8$ counters is equally likely. That is what makes it safe to work the probability out by counting outcomes.

Write down the probability

For equally likely outcomes the probability is the number of favourable outcomes over the total: $\frac{5}{8}$. $5$ and $8$ have no common factor bigger than $1$, so it is already in its simplest form. The favourable outcomes are the $5$ red counters.

State the answer

So the probability that a red counter is taken is $\frac{5}{8}$.

Check that the outcomes are equally likely

The question says the counter is fair, so each of the $20$ counters is equally likely. That is what makes it safe to work the probability out by counting outcomes.

Write down the probability and simplify it

For equally likely outcomes the probability is the number of favourable outcomes over the total: $\frac{4}{20}$. The highest common factor of $4$ and $20$ is $4$, so this simplifies to $\frac{1}{5}$. The favourable outcomes are the $4$ blue counters.

State the answer

So the probability that a blue counter is taken is $\frac{1}{5}$.