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Statistical independence

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Events A and B are said to be independent if the probability of A occurring is not affected by the probability of B occurring and vice versa.

Formula

Two events are said to be independent if the probability of both events occurring is equal to the multiple of the probabilities of each event.

Independence.png

Examples

  • Rolling a 2 on a fair 6 sided die, and then rolling a 3 on second try. The probability of getting a 2 on the first roll is not affected by the probability of getting a 3 on the second roll, or vice versa.
  • The outcome of subsequent coin tosses are independent of previous outcomes. i.e. the probability of getting a head or tail on a fair coin is always the same regardless of the outcome of previous tosses.