# Video: GCSE Mathematics Foundation Tier Pack 5 • Paper 2 • Question 23

GCSE Mathematics Foundation Tier Pack 5 • Paper 2 • Question 23

02:28

### Video Transcript

There are 30 boys and 36 girls in a year group. One-sixth of the boys and one-third of the girls are left-handed. A teacher picks a left-handed child at random. Calculate the probability that this child is a girl.

We’re told that the teacher picks a left-handed child at random, which means that all of the left-handed children in the year group have an equal chance of being chosen. To calculate the probability that this child is a girl then, we need to find the number of left-handed girls in the year group and divide this by the total number of left-handed children.

Now, we haven’t been given either of these pieces of information explicitly in the question. But we have been given enough information to work them out. Let’s look at the girls first of all. We’re told that there are 36 girls in the year group and one-third of them are left-handed. So to find the number of left-handed girls in the year group, we need to find one-third of 36.

The easiest way to find one-third of a number is just to divide it by three. 36 divided by three is 12. We know that because this is one of our times tables, that three multiplied by 12 is 36. So the reverse of that tells us that 36 divided by three is 12 or we could use a short division or bus stop method to work this out. So the number of left-handed girls in the class is 12.

For the boys, we’re told that there are 30 boys in a year group and one-sixth of them are left-handed. So we need to find one-sixth of 30. To find one-sixth of a number, we divide by six and 30 divided by six is five. This is again one of our times tables that five multiplied by six is equal to 30.

To find the total number of left-handed children in the year group then, we add the 12 girls to the five boys and we have 17. So the number of left-handed girls in the year group is 12 and the total number of left-handed children in the year group is 17, which means that the probability that the randomly chosen left-handed child will be a girl is 12 over 17 or twelve seventeenths.

We can leave answer as a fraction. And as 12 and 17 don’t have any common factors other than one, this fraction is already in its simplest form and can’t be cancelled down any further. So our final answer is twelve seventeenths.