| Concept | Formula | Description |
|---|---|---|
| Classical Probability | P(A) = Number of favorable outcomes / Total number of outcomes | Probability based on equally likely outcomes. Example: Probability of rolling a 3 on a fair die is 1/6. |
| Relative Frequency Probability | P(A) = Number of times event A occurs / Total number of trials | Relative frequency probability is calculated based on the frequency of the event occurring in a series of trials. Example: If a survey finds that 150 out of 1,000 respondents prefer a certain brand, the probability of a randomly selected person preferring that brand is P(Preference) = 150/1000 = 0.15. |
| Addition Rule | P(A ∪ B) = P(A) + P(B) – P(A ∩ B) | Used to find the probability of either event A or B occurring. Example: Probability of drawing a heart or a queen from a deck of cards. |
| Complement | P(A’) = 1 – P(A) | The probability of event A not occurring. Example: If the chance of rain is 0.3, then the chance of no rain is 0.7. |
| Multiplication Rule | P(A ∩ B) = P(A) × P(B | A) | Used when two events are dependent. Example: Probability of drawing two aces in a row from a deck of cards, without replacement. |
| Conditional Probability | P(A | B) = P(A ∩ B) / P(B) | Probability of A given B has occurred. Example: Probability of a randomly chosen person being a doctor, given they are a teacher. |
| Bayes’ Rule | P(A | B) = P(B | A) × P(A) / P(B) | Used to revise probabilities given new information. Example: Revising the probability of a disease given a positive test result. |
| Odds Ratio | P(A) / (1 – P(A)) for event A | Ratio of the probability of an event occurring to it not occurring. Example: If a horse has a 0.8 probability of winning, the odds are 4 to 1. |
Basics of Probability – Summary Sheet
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