Introduction to Probability
Probability is defined as
A value between
0 and 1 that quantifies the likelihood of an event occurring- A probability of
0means the event is impossible.
- A probability of
1means the event is certain.
Ā
Mathematically, if is an event within a sample space , the probability of , denoted , is expressed as:
For example, if a standard six-sided die is rolled, the probability of rolling a
4 is:Interpretations of Probability
The concept of probability can be interpreted in different ways depending on the context:
- Frequentist Interpretation: Probability is understood as the long-run relative frequency of an event occurring in repeated independent trials. For instance, if we flip a fair coin many times, we expect the proportion of heads to converge to
0.5.
- Bayesian Interpretation: Probability represents a degree of belief or certainty about an event, which can be updated as new information becomes available. For example, a weather forecast might say thereās a
70%chance of rain tomorrow, reflecting the meteorologist's confidence based on current data.
Example
In a deck of
52 playing cards, the probability of drawing an Ace is: