Probability of Mutually Exclusive and Non-Mutually Exclusive Events

Mutually Exclusive Events

• Definition: Mutually exclusive events are events that cannot occur at the same time. In other words, they have no outcomes in common.

• Probability Formula: The probability of either event A or event B occurring is the sum of their individual probabilities. $P(A \text{ or } B) = P(A) + P(B)$

  • Where:

    • $P(A \text{ or } B)$ is the probability of either A or B occurring

    • $P(A)$ is the probability of event A occurring.

    • $P(B)$ is the probability of event B occurring.

Non-Mutually Exclusive Events

• Definition: Non-mutually exclusive events are events that can occur at the same time. They have some outcomes in common.

• Probability Formula: The probability of either event A or event B occurring is the sum of their individual probabilities minus the probability of both A and B occurring. $P(A \text{ or } B) = P(A) + P(B) - P(A \text{ and } B)$

  • Where:

    • $P(A \text{ or } B)$ is the probability of either A or B occurring

    • $P(A)$ is the probability of event A occurring.

    • $P(B)$ is the probability of event B occurring.

    • $P(A \text{ and } B)$ is the probability of both A and B occurring.