Never happens
An impossible event has probability 0.
Hoping for an 8
The faces of a fair die are marked 1, 2, 3, 4, 5 and 6. You throw it once and hope to get an 8.
What is the probability of getting an 8?
What this lesson covers
The idea
An event that cannot occur has no favourable outcomes; it is called an impossible event and its probability is 0.
Hoping for an 8
The faces of a fair die are marked 1, 2, 3, 4, 5 and 6. You throw it once and hope to get an 8.
What is the probability of getting an 8?
- 1/6
- 0
- 1/8
Find an event with no favourable face
The dial k decides the event E, "getting k". The lit faces are the favourable ones. Turn the dial until no face is favourable.
No favourable outcome, probability 0
An event that cannot occur has no favourable outcomes. It is called an impossible event, and its probability is 0.
No face of a die is marked 8, so the number of favourable outcomes is 0, and P(getting 8) = 0/6 = 0. The top of the fraction is 0, so the whole fraction is 0.
The same happens with two dice. The biggest sum is 6 + 6 = 12, so none of the 36 outcomes has sum 13: P(sum is 13) = 0/36 = 0.
Notes
An event that cannot occur has no favourable outcomes. It is an impossible event, and P(E) = 0.
Check yourself
A die is thrown once. Which event is impossible?
Two dice, one blue and one grey, are thrown at the same time. Find the probability that the sum of the two numbers is 13.
Answer: 0
The biggest sum is 6 + 6 = 12, so 0 outcomes are favourable: P = 0/36 = 0.
A box has 3 blue, 2 white and 4 red marbles. One marble is drawn at random. Find the probability that it is green.
Answer: 0
There is no green marble, so 0 outcomes are favourable: P(green) = 0/9 = 0.
For an event E, P(E) = 0. What do we know?
- getting an even number. The faces 2, 4 and 6 are favourable, so this can happen. P = 3/6.
- getting a 6. The face 6 is favourable, so this can happen. P = 1/6.
- getting a number greater than 6 — correct. Yes! No face shows a number greater than 6, so there are 0 favourable outcomes: P = 0/6 = 0.
- E can never happen: no outcome is favourable to it — correct. Yes! P(E) = 0 means the number of favourable outcomes is 0.
- E is very unlikely, but it can happen. If an outcome were favourable, the number of favourable outcomes would be at least 1, and P(E) would be more than 0.
- E happens in half of the trials. That would be P(E) = 1/2.