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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 \(P(A \cup B) = P(A) + P(B) - P(A \cap B)\)
The views expressed in the notes here are those of the contributor and don’t necessarily represent the views of pandai.

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 \(P(A \cup B) = P(A) + P(B) - P(A \cap B)\)
The views expressed in the notes here are those of the contributor and don’t necessarily represent the views of pandai.
Chapter : Probability of Combined Events
Topic : Mutually Exclusive Events and Non-Mutually Exclusive Events
Form 4 Mathematics
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