05 / 10 · Probability
What is probability?
Counting the ways things can happen
Probability is a number between 0 and 1 that says how likely something is. 0 means it cannot happen, 1 means it is certain, and 0.5 means it is as likely as not.
When every outcome is equally likely, like the faces of a fair die, probability is just counting. List everything that can happen (the sample space), count the outcomes you care about (the event), and divide.
P(event) = favourable outcomes ÷ all outcomes P(even) = 3 ÷ 6 = 0.5 P(> 4) = 2 ÷ 6 ≈ 0.33
Try it · Choose an event. The faces that make it happen turn orange and the probability appears on the 0 to 1 scale. Press Roll to try your luck.
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Rolling an even number: three good faces (2, 4, 6) out of six, so the probability is 3/6 = 1/2. Rolling a 7: no faces at all, so 0/6 = 0.
This is called the classical definition, and it only works when outcomes really are equally likely. A loaded die breaks it, which is why we will need other ideas later.
Key ideas
Words worth remembering
- Sample space
- The list of everything that can happen.
- Event
- The group of outcomes you are asking about.
- Probability
- A number from 0 (impossible) to 1 (certain).
Think about it
Is the probability of rolling a 6 the same as the probability of not rolling a 6?