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1.9

## Cambridge University Press

Use your spinner to collect some data.

# Collecting data

Now you can use your paperclip and the supplied spinner template to collect some experimental data.

We are going to use the spinner as a tool to explore a very simple mathematical model: what is the weather going to do? However, before we launch into an experiment to collect data to investigate this model, we need to clarify some key terms.

Suppose we define blue on the spinner to mean a rainy day, and yellow to mean a sunny day. These are the only two outcomes of a single spin. This list of all the possible outcomes is the sample space:

• Blue = rainy (R)
• Yellow = sunny (S)

Now suppose that we make our model slightly more complex, by having two spins for each day - one to represent the morning weather, and one for the afternoon. Our sample space now consists of four outcomes:

• RR
• RS
• SR
• SS

Next, we need to talk about trials. In our experiment, a single trial will consist of two spins - one spin to determine the weather on the morning of a particular day, and another spin for the afternoon.

Suppose we want to know on how many occasions in 25 days it rains at some point in the day. We have now defined the event ‘some rain’ as a particular subset of the sample space (the outcomes which include rain). We will need to carry out 25 trials (so 50 spins altogether), and find the total frequency of the outcomes RR, SR, and RS.

Now carry out the experiment, and use your results to estimate the probability of the event ‘some rain’.