Probability of Union of Two Events
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Questions and Answers

What is the probability of the intersection of two events A and B when they are independent?

  • P(A) × P(B) (correct)
  • P(A) - P(B)
  • P(A) / P(B)
  • P(A) + P(B)

    • What does P(A ∩ B) represent?

  • The probability of both events A and B occurring (correct)
  • The probability of event B but not event A
  • The probability of event A but not event B
  • The probability of event A or event B occurring

    • What is the definition of mutually exclusive events?

  • Events that are independent of each other
  • Events that are dependent on each other
  • Events that always occur together
  • Events that never occur together (correct)

    • What is the formula for the probability of the intersection of two events A and B?

    <p>P(A) × P(B|A)</p> Signup and view all the answers

    What is the probability of the intersection of two mutually exclusive events A and B?

    <p>0</p> Signup and view all the answers

    What does P(A|B) represent?

    <p>The probability of event A given event B</p> Signup and view all the answers

    When are two events A and B considered independent?

    <p>When the occurrence of one event does not affect the probability of the other</p> Signup and view all the answers

    What is the probability of the union of two events A and B, denoted as A ∪ B?

    <p>The probability of event A or event B occurring</p> Signup and view all the answers

    What is the formula for the probability of the intersection of two independent events A and B?

    <p>P(A) × P(B)</p> Signup and view all the answers

    Study Notes

    Probability of Union of Two Events

    Intersection of Events

    • The intersection of two events A and B, denoted as A ∩ B, represents the occurrence of both events.
    • The probability of the intersection of two events is denoted as P(A ∩ B).
    • The probability of the intersection of two events can be calculated using the formula:
    P(A ∩ B) = P(A) × P(B|A) = P(B) × P(A|B)

    Where P(A|B) is the conditional probability of event A given event B, and P(B|A) is the conditional probability of event B given event A.

    Independent Events

    • Two events A and B are said to be independent if the occurrence of one event does not affect the probability of the other event.
    • If A and B are independent, then:
    P(A ∩ B) = P(A) × P(B)
    • In other words, the probability of the intersection of two independent events is the product of their individual probabilities.

    Mutually Exclusive Events

    • Two events A and B are said to be mutually exclusive if they cannot occur simultaneously.
    • If A and B are mutually exclusive, then:
    P(A ∩ B) = 0
    • In other words, the probability of the intersection of two mutually exclusive events is zero.

    Probability of Union of Two Events

    • The probability of the union of two events A and B, denoted as A ∪ B, represents the occurrence of at least one of the events.
    • The probability of the union of two events can be calculated using the formula:
    P(A ∪ B) = P(A) + P(B) - P(A ∩ B)
    • Note that if A and B are mutually exclusive, then P(A ∩ B) = 0, and the formula simplifies to:
    P(A ∪ B) = P(A) + P(B)

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    Description

    Learn about the intersection and union of two events, independence, and mutual exclusivity in probability theory. Understand the formulas and concepts to calculate probabilities.

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