# Video: AQA GCSE Mathematics Foundation Tier Pack 4 • Paper 1 • Question 18

Here is a fair six-sided spinner. (a) Write down the probability that the arrow lands on three with one spin. (b) The spinner is spun twice. The numbers shown by the arrow at each spin are added up. Work out the probability that the sum is 6.

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### Video Transcript

Here is a fair six-sided spinner. Part a) Write down the probability that the arrow lands on three with one spin. Part b) The spinner is spun twice. The numbers shown by the arrow at each spin are added up. Work out the probability that the sum is six.

As the spinner is fair, there is an equal chance that it will land on each number, the numbers one, two, three, four, five, and six. The probability of an event occurring can be written as a fraction, where the numerator is the number of successful outcomes and the denominator is the number of possible outcomes.

In part a of the question, we want to work out the probability that the spinner lands on three. There is only one number three on the spinner. Therefore, there is one successful outcome. As there are six numbers altogether on the spinner, there’re six possible outcomes. This means that the probability that the arrow lands on three with one spin is one out of six or one-sixth. This probability is the same for landing on any of the other numbers.

The second part of the question says that the spinner is spun twice. The two numbers are added up. And we need to calculate the probability that the sum is six. One way of approaching any problem like this is to set up a two-way table. On the first spin, the arrow can point to any of the numbers from one to six. On the second spin, it can also land on any of the numbers from one to six. These two events are independent as one has no impact on the other.

In order to complete the two-way table, we need to add the score on the first spin to the score on the second spin. Adding the numbers in the top row gives us two, three, four, five, six, and seven. The second row becomes three, four, five, six, seven, and eight. The rest of the table can be completed as shown. We need to work out the probability that the sum is six.

There are five sixes in the table as we can get a sum of six by spinning one and five, two and four, three and three, four and two, and five and one. This means that the number of successful outcomes is five. So the numerator of our fraction will be five. There are 36 numbers altogether in the table. Therefore, the denominator, the number of possible outcomes, is 36.

Another way of calculating the number of possible outcomes would be to multiply the number of outcomes on the first spin by the number of outcomes on the second spin. Six multiplied by six is equal to 36. If the spinner is spun twice, the probability that the sum is six is five out of 36 or five 36ths.