Determine the probability of combined events for mutually exclusive and non-mutually exclusive events.

Mutually Exclusive Events and Non-Mutually Exclusive Events

9.3

Mutually Exclusive Events and Non-Mutually Exclusive Events

Mutually Exclusive Events and Non-Mutually Exclusive Events

A combined event \(A\) and \(B\) is known as a mutually exclusive event if there is no intersection between events \(A\) and \(B\), \(A \cap B \neq \emptyset\).

Verify the Formula of Probability of Combined Events for Mutually Exclusive and Non-Mutually Exclusive Events

Formula

The combined event \(A\) and \(B\) is non-mutually exclusive because \(P(A \cap B) \neq 0\), \(P(A \space \text{or} \space B) = P(A) + P(B) - P( A\cap B)\).

The combined event \(A\) and \(B\) is non-mutually exclusive because \(P(A \cap C) \neq 0\) and \(P(B\cap C) =0\), then \(P(A \space \text{or} \space C) = P(A) + P(C) \space \text{and} \space P(B \space \text{or} \space C)= P(B) + P(C)\).

Addition Rule of Probability

\(P(A \cup B) = P(A) + P(B) \) or \(P(A \cup B) = P(A) + P(B) - P(A \cap B)\)

Mutually Exclusive Events and Non-Mutually Exclusive Events

9.3

Mutually Exclusive Events and Non-Mutually Exclusive Events

Mutually Exclusive Events and Non-Mutually Exclusive Events

A combined event \(A\) and \(B\) is known as a mutually exclusive event if there is no intersection between events \(A\) and \(B\), \(A \cap B \neq \emptyset\).

Verify the Formula of Probability of Combined Events for Mutually Exclusive and Non-Mutually Exclusive Events

Formula

The combined event \(A\) and \(B\) is non-mutually exclusive because \(P(A \cap B) \neq 0\), \(P(A \space \text{or} \space B) = P(A) + P(B) - P( A\cap B)\).

The combined event \(A\) and \(B\) is non-mutually exclusive because \(P(A \cap C) \neq 0\) and \(P(B\cap C) =0\), then \(P(A \space \text{or} \space C) = P(A) + P(C) \space \text{and} \space P(B \space \text{or} \space C)= P(B) + P(C)\).

Addition Rule of Probability

\(P(A \cup B) = P(A) + P(B) \) or \(P(A \cup B) = P(A) + P(B) - P(A \cap B)\)

Chapter : Probability of Combined Events

Topic : Determine the probability of combined events for mutually exclusive and non-mutually exclusive events.