```
import pandas as pd
```

# Two Special Events¶

There are two particularly important events that we must notice:

The event of **"nothing happening"**, which means we make an experiment and nothing happens. We are going to represent it with the empty set: $\emptyset$.

The event of **"anything happening"**, which means we make an experiment and something happens. We are going to represent it with the full set Omega: $\Omega$.

Of course that it is impossible that nothing happens when we perform an experiment: we might not know *what* will happen if we are performing a random experiment, but we certainly know that *something* will.

We have already said that the probability of impossible outcomes is $0$ (remember the probability scale) so, as expected, the probability of $\emptyset$ will be $0$.

On the other hand, when we perform an experiment, we are certain that we will get some outcome, *something* will happen. So if we just want *anything* to happen, we can be sure that will be the case.

And we have said that the probability of certain outcomes is $1$ (remember the probability scale) so, as expected the probability of $\Omega$ will be $1$.

Summarising:

### $P(\emptyset)=0$ and $P(\Omega)=1$.¶

Before going to practise, let's see this in our example:

```
dataset = pd.DataFrame({
'Person #':[1,2,3,4,5,6,7,8,9,10],
'City':['SF','SF','NY','NY','NY','SF','NY','SF','SF','SF'],
'Age':[41,26,28,53,32,51,65,49,25,33]
})
dataset
```

```
dataset.sample(1)['Age'].values[0]
```

Now imagine we have the event $E=$ "the person chosen is younger than $20$". We can tell that this event actually contains no age at all, because our ages start at $25$. So $P(E)=P(\emptyset)=0$.

In the case of, for example, the event $F=$ "the person chosen is younger than $70$" we can see that it contains all possible ages, because our ages finish at $65$. So $P(F)=P(\Omega)=1$.