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Independent events

Two events are independent when one does not change the probability of the other. Then the probability of both is the product of the probabilities. A tree diagram with one number on each branch shows the same thing. If the events are dependent, as in drawing without replacement, you cannot just multiply the original probabilities. Write down whether the trials affect each other.

P(A∩B)=P(A)⋅P(B)P(A \cap B) = P(A) \cdot P(B)independent events

Symbols

P(A)P(A)probability of A
P(B)P(B)probability of B

Example

The probability of rain is 0.3 and of the bus being late 0.4, independently.

P(both)=0.3⋅0.4=0.12P(\text{both}) = 0.3 \cdot 0.4 = 0.12.

Independent: multiply. Dependent: calculate the conditional probability.
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Part of Mathematics S1: Probability.