Quick Answer: Probability is the mathematical measure of how likely an event is to happen, expressed as a number between 0 (impossible) and 1 (certain). To calculate simple probability: Target Outcomes ÷ Total Possible Outcomes. Example: Probability of flipping heads is 1 ÷ 2 = 0.5 (50%).
What exactly is probability?
Probability answers the question: "If I do this experiment, how likely is this specific result?" It uses a scale from 0 to 1, though we often express it as percentages (0% to 100%). If P=0, the event will never happen. If P=1, it will definitely happen. If P=0.5, it happens half the time.
The Core Formula
For any simple random event where all outcomes are equally likely, you find probability by counting: Probability (P) = Number of Ways it Can Happen ÷ Total Number of Outcomes.
- Coin flip: 1 way to get heads ÷ 2 total outcomes = 1/2 or 50%
- Rolling a 6 on a die: 1 face with a 6 ÷ 6 total faces = 1/6 or 16.67%
- Rolling an even number: 3 even faces (2,4,6) ÷ 6 total faces = 3/6 = 50%
- Picking a heart from a deck: 13 hearts ÷ 52 total cards = 13/52 = 25%
Theoretical vs. Experimental Probability
Theoretical probability is what the math says SHOULD happen (like a coin being 50/50). Experimental probability is what ACTUALLY happens when you run trials (like flipping a coin 10 times and getting 7 heads, which is 70%). The Law of Large Numbers explains that as you run more experiments, experimental probability gets closer and closer to theoretical probability.
Independent vs. Dependent Events
| Type | Definition | Example |
|---|---|---|
| Independent | The outcome of one event does not affect the next. | Flipping a coin twice. The second flip is still 50/50. |
| Dependent | The outcome of one event changes the probability of the next. | Drawing cards without putting them back. |