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Math Help - Definition of Complement

  1. #1
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    Definition of Complement

    I'm having trouble understanding the following:

    Definition of Complement-image.png

    Does Ec mean that all events in the sample space (besides E) necessarily happen, or simply that E does not happen? In other words, if the sample space is S={A,B,C,D,E} does Ec imply A,B,C, and D have occurred, or just that E hasn't occurred?
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  2. #2
    Junior Member Bradyns's Avatar
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    Re: Definition of Complement

    What your image is implying, is that if you have an event E, visa-vi a probability.

    Then if E doesn't happen, you have E^{c}.

    If you have a set of events A, B, C, D and E.

    Then E^{c} is simply the case where E doesn't happen.

    It doesn't mean that the others necessarily happen, nor does it tells us the individual probability of each.

    If P(E) = 0.2, then at most, we can say that P(E^{c}) = 0.8, or P(E^{c}) = P(A) + P(B) + P(C) + P(D) = 0.8.
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  3. #3
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    Re: Definition of Complement

    Perfect. Exactly the clarification I needed.
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