Definition
Impossible event
An impossible event contains no outcomes in the stated sample space.
What it means
Check the complete list of possible outcomes. If none of them can make the event happen, the event is impossible for that model. This is stronger than being very unlikely.
Remember it
No outcome in the box can make it happen.
Example
A spinner has sections labelled A, B, and C. The event “land on D” is impossible because D is not in the spinner’s sample space.
Watch for
Drawing the only gold counter from a bag of 1 gold and 99 silver counters is very unlikely, but it is possible because gold is in the sample space.
Common mix-up
Impossible depends on the stated model. Changing the spinner, die, bag, or rules can change which events are impossible.
Exact meaning
In a stated probability model, an impossible event is the empty event: no possible outcome makes it occur. Therefore its probability is 0.