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

There are possible sequences, so .

To count the number of possible subsets, consider that we have 32 distinct items, and a subset is uniquely determined by the binary information – for each item – of whether it is in or out. Thus there are possibilities. So .