Probability Cheat Sheet

Key Definitions

• Probability: Measure of the likelihood of an event occurring, ranging from 0 (impossible) to 1 (certain).

• Experiment: A procedure that yields one of a possible set of outcomes.

• Sample Space (S): The set of all possible outcomes of an experiment.

• Event: A subset of the sample space.

Important Concepts

Types of Events

• Simple Event: Contains exactly one outcome.

• Compound Event: Contains two or more outcomes.

• Independent Events: The occurrence of one event does not affect the other.

• Dependent Events: The occurrence of one event affects the other.

Complementary Events

• If A is an event, then its complement is denoted as A'.

• P(A) + P(A') = 1

Key Formulas

• Probability of an Event:

P(A) = (Number of favorable outcomes) / (Total number of outcomes)

• Addition Rule:

P(A or B) = P(A) + P(B) - P(A and B)

• Multiplication Rule:

P(A and B) = P(A) * P(B) (if A and B are independent)

Common Mistakes to Avoid

Common Mistake: Forgetting to account for the total number of outcomes when calculating probabilities.

Memory Tricks

Tip: "SOME" — Sample space, Outcomes, Multiplication rule, Event probabilities.

Key Diagrams

Sample Space (S)
+-----------------+
| 1 | 2 | 3 | 4 | 5 |
+-----------------+
Event A: {1, 2}
Event B: {2, 3}