Examples

Coin flipping

Flip a fair coin two times and record both results.

• Outcomes: sequences, like or .

• Sample space: all possible sequences, i.e. the set .

• Events: for example:

With this setup, we may combine events in various ways to generate other events:

Complex events: for example: , or in words:

Notice that the last one is a complete description, namely the outcome . , or in words:

Coin flipping: counting subsets

Flip a fair coin five times and record the results.

How many elements are in the sample space? (How big is ?) How many events are there? (How big is ?)

Solution