Independent events

If two events are independent, it means that the probability of each event does not depend on the outcome of the other event.

This effectively means that:

• the probability of event A is the same regardless of whether event B occurs or not, and vice-versa.

Some facts about independent events

• The probability of both events A and B occurring is the product of their individual probabilities.
  • P(A \cap B) = P(A) \times P(B)
• The probability of either event A or B occurring is the sum of their individual probabilities minus the probability of both events occurring.
  • P(A \cup B) = P(A) + P(B) - P(A \cap B)
• Using both of those rules above, we can write the probability of either A occurring or B occurring as:
  • P(A \cup B) = P(A) + P(B) - P(A) \times P(B)