Basic probability
Measure luck with math
What is this about?
Probability measures how likely something is to happen, with a number between 0 (impossible) and 1 (certain). When all outcomes are equally likely (like the faces of a die), you use Laplace's rule: favorable outcomes divided by possible outcomes.
The rule to remember
Probability = favorable outcomes ÷ possible outcomes. First count ALL possible outcomes, then how many work for you, and divide. The result is always between 0 and 1: if you get more than 1, you counted something wrong.
Example 1
P(rolling a 3 with one die)
- 1Possible outcomes: the die has 6 faces → 6 outcomes.
- 2Favorable outcomes: only one face shows a 3 → 1 outcome.
- 3Apply Laplace: P = 1 ÷ 6 = 1/6 ≈ 0.17.
- 4It's closer to 0 than to 1: rolling one specific number isn't easy.
Result: 1/6
Example 2
P(drawing a red ball from a bag with 3 red and 2 blue)
- 1Possible outcomes: 3 + 2 = 5 balls in total.
- 2Favorable outcomes: 3 red balls.
- 3P = 3 ÷ 5 = 3/5 = 0.6.
- 4Since 0.6 is past the halfway mark, red is MORE likely than blue.
Result: 3/5
The most common mistake
Many people write
P(even number on a die) = 3/3 = 1
Why it's wrong
The favorable outcomes (2, 4, 6) were also counted as the possible ones. The possible outcomes are ALL the faces: 6. The correct probability is 3/6 = 1/2. A probability of 1 would mean it's certain, and it isn't.
Did it click?
The best way to find out is to try. These exercises are exactly on this topic.
Practise this topic