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sasogeek

  • 3 years ago

Probability: Two events A and B are such that \(\large P(A \) U \(\large B)=\frac{11}{15} \) and \(\large P(A)=\frac{1}{3} \) : Find \(\large P(B) \) if the events A and B are a. Mutually exclusive b. Independent

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  1. across
    • 3 years ago
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    Let \(A\) and \(B\) be mutually exclusive events. Then the identity\[P(A\cup B)=P(A)\cup P(B)-P(A\cap B)\]becomes\[P(A\cup B)=P(A)\cup P(B).\] Similarly, let \(A\) and \(B\) be independent events. Then the identity\[P(A\cup B)=P(A)\cup P(B)-P(A\cap B)\]becomes\[P(A\cup B)=P(A)\cup P(B)-P(A)P(B).\] Finally, all you have to do is perform very simple algebra to find \(P(B)\).

  2. sasogeek
    • 3 years ago
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    Thank you:) though I figured the answer just a couple of minutes after asking. I'm glad you answered though, someone **MAY** need it. :P

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