Curriculum
Statistics — Third Secondary
Unit 1: Correlation and Regression
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Unit 2: Advanced Statistical Measures
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Unit 3: Probability
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Unit 4: Random Variables
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Unit 5: The Normal Distribution
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Text lesson
Conditional Probability and Independent Events
Conditional Probability and Independent Events
Independent events and mutually exclusive events
Independent events and mutually exclusive events
- Two events are independent when the occurrence of one does not affect the probability of the other, and both can occur together.
- Two events are mutually exclusive when they cannot occur together in the same experiment.
- The table below shows the difference:
| Comparison | Independent events | Mutually exclusive events |
|---|---|---|
| Meaning | One occurring does not change the probability of the other | They cannot occur together |
| Probability of intersection | P(A ∩ B) = P(A) × P(B) | P(A ∩ B) = 0 |
| Conditional probability | P(A | B) = P(A) | P(A | B) = 0 |
- To test whether two events are independent
- we check one of the two equivalent conditions:
P(A ∩ B) = P(A) × P(B), or
- P(A | B) = P(A), where P(B) ≠ 0.
- Note that two mutually exclusive events are not independent, unless the probability of one of them is zero.
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