Learning Objective
Understand and apply key probability rules, including calculations for independent and mutually exclusive events, as well as adjustments for nonindependent and non-mutually exclusive scenarios.
Independent Events
Definition: Two events are independent if the occurrence of one event does not affect the probability of the other.
Rule: Multiply the probabilities of the individual events to find the probability of both occurring:
Example:
- Probability of having blond hair: P(Blonde)=0.3
- Probability of having a cold: P(Cold)=0.2
The probability of meeting someone with both blond hair and a cold is:
Non-independent events:
If events are dependent, multiply the probability of the first event by the conditional probability of the second:
Example:
Picking 2 black balls from a box with 5 white and 5 black balls:
Mutually Exclusive Events
Definition: Two events are mutually exclusive if the occurrence of one prevents the occurrence of the other.
Rule: Add the probabilities of the events:
Example:
Flipping a coin:
Non-mutually exclusive events
If events can occur together, add the probabilities and subtract the overlap:
Example:
Probability of someone being diabetic or obese:
