- Calculate the probability of an event in a chance experiment.
- Recognize the differences between theoretical and empirical probability.
Probability Values
Probability is always a value from [latex]0[/latex] to [latex]1[/latex], inclusive (which means that [latex]0[/latex] and [latex]1[/latex] are included). We can write probability as a fraction, a decimal, or a percentage from [latex]0\%[/latex] to [latex]100\%[/latex], inclusive.
So, for event [latex]A[/latex]:
[latex]0 \le P(A) \le 1[/latex]
or
[latex]0\% \le P(A) \le 100\%[/latex]
In the world of probabilities, numbers between [latex]0[/latex] and [latex]1[/latex] hold special significance. These numbers represent the likelihood or chance of an event occurring. It allows us to express how likely or unlikely an event is, offering a clear and intuitive framework for reasoning about uncertainty and making informed decisions based on the likelihood of various outcomes.
| Probability Range | 0 | (0, 0.5) | (0.5, 1) | 1 |
|---|---|---|---|---|
| Event Likelihood | Impossible | Improbable | Probable | Certain |
- Impossible Event: This is when the probability of an event is 0. It means that there is no chance that the event will happen.
-
Improbable Event: This is when the probability of an event is greater than 0 but less than 0.5. These events are not expected to happen often, but they are not impossible.
-
Probable Event: This is when the probability of an event is greater than 0.5 but less than 1. These events are more likely to happen than not.
-
Certain Event: This is when the probability of an event is 1. This means that the event is guaranteed to happen.
- Find [latex]P(\text{either getting a head or a tail})[/latex].
- Find [latex]P(\text{land on an edge})[/latex].
- To put it simply, if an event is impossible, its probability is [latex]0[/latex].
- Conversely, if an event is certain to happen, its probability is [latex]1[/latex].