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Independent trials

Two trials are independent when the first does not change the probability of the second. Then the probability of both is the product of the probabilities. A coin toss does not change the next one. A tree diagram with a probability on each branch shows the same products. If you draw without replacement, the trials are dependent, and you cannot multiply the same numbers again.

P(A and B)=P(A)⋅P(B)P(A \text{ and } B) = P(A) \cdot P(B)independent

Symbols

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

Example

Two coin tosses. The probability of heads both times is 0.5⋅0.5=0.250.5 \cdot 0.5 = 0.25.

Independent: multiply. Without replacement: the probability changes.
Practise probability for free →

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Part of Mathematics 1P: Probability.