Probability: Mutually Exclusive Events

Study Notes

Mutually exclusive events are events that cannot occur at the same time. If one event happens, the other cannot.
The probability of both events happening simultaneously is zero.
Mathematically, if A and B are mutually exclusive events, then P(A and B) = 0.
Example: Rolling a die. Getting a '1' and getting a '6' are mutually exclusive events. You can't have both outcomes on one roll.
The addition rule for mutually exclusive events states: P(A or B) = P(A) + P(B). This rule applies only to mutually exclusive events.

Non-mutually exclusive events are events that can occur at the same time.
The probability of both events happening simultaneously is greater than zero, but may not be equal to 1.
Example: Drawing a card from a deck. Drawing a 'heart' and drawing a 'face card' are non-mutually exclusive events. A card could be both a heart and a face card (e.g., the Jack of Hearts).
The addition rule for mutually exclusive events does not apply to non-mutually exclusive events.
The probability that either event A or event B occurs, or both occur is calculated as: P(A or B) = P(A) + P(B) - P(A and B). The subtracted term, P(A and B), accounts for the overlap, the events happening at the same time.
This is a crucial distinction as the overlap in probability needs to be considered. Overlapping events increase the probability that either event will occur.
Understanding the difference between mutually exclusive and non-mutually exclusive events is essential in calculating probabilities accurately and correctly applying the addition rule.