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)

Question	Answer
What defines two events as independent?	The probability of each event does not depend on the outcome of the other event.
How does the probability of event A change regarding event B for independent events?	The probability of event A is the same regardless of whether event B occurs or not.
What is the formula for P(A \cap B) for independent events?	P(A \cap B) = P(A) \times P(B)
What is the formula for P(A \cup B) for independent events using individual probabilities?	P(A \cup B) = P(A) + P(B) - P(A \cap B)
How do you write P(A \cup B) for independent events using only P(A) and P(B)?	P(A \cup B) = P(A) + P(B) - P(A) \times P(B)