| 9.3 |
Mutually Exclusive Events and Non-Mutually Exclusive Events |
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- A combined events \(A\) and \(B\) is known as a mutually exclusive event if there is no intersection between events \(A\) and \(B\), \(A \cap B \neq \emptyset\)
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| Verify a formula of probability of combined events for mutuallay exclusive and non-exclusive events |
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Formulae |
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- The combined event \(A\) and \(B\) is non-mutually exclusive because \(P(A \cap B) \neq 0\), then \(P(A \space \text{or} \space B) = P(A) + P(B) - P( A\cap B)\)
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- The combined event \(A\) and \(B\) is non-mutually exclusive because \(P(A \cap C) \neq 0\) and \(P(B\cap C) =0\), then \(P(A \space \text{or} \space C) = P(A) + P(C) \space \text{and} \space P(B \space \text{or} \space C)= P(B) + P(C)\)
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The addition rule of probability is
\(P(A \cup B) = P(A) + P(B) \) or \(P(A \cup B) = P(A) + P(B) - P(A \cap B)\)
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Example |
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