Solution

a) The sample space is $ \{ \text{heads,} \text{ tails} \} $.

b) The sample space is $ \{ 0,1,2,3 \}$.

c) The sample space consists of every single length of time from $13.2$s to $17.4$s.

In the last example, we have a continuous set, how do we represent this? We cannot write down every single number. Using the same notation as above, a perfectly good representation would be \[\{ \textrm{All times from } 13.2s \textrm{ to } 17.4s \}.\]

While there is technically nothing wrong with this, we can simplify it using a variable, say $t$, where $t$ is the number of seconds taken to run 100m.

\[\{t : 13.2\leq t \leq 17.4 \}.\]

Here, the “$:$” sign means “such that”. So, in English, we say “$t$ such that $t$ is between $13.2$ and $17.4$ inclusive”.