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    patsygee1's Avatar
    patsygee1 Posts: 3, Reputation: 1
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    #1

    Aug 16, 2009, 10:38 AM
    mutually exclusive
    The events X and Y are mutually exclusive. Suppose P(X) _ .05 and P(Y) _ .02. What is
    the probability of either X or Y occurring? What is the probability that neither X nor Y will
    happen?
    s_cianci's Avatar
    s_cianci Posts: 5,472, Reputation: 760
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    #2

    Aug 16, 2009, 10:44 AM
    If they're mutually exclusive, then that means they can't both happen ; if one happens, then the other doesn't and vice-versa. You have the individual probabilities for both X and Y. So it should now be easy to calculate the either/or probability. And once you have that answer, it's easy to determine the neither/nor probability as that's simply the complementary event to the either/or probability. I'm not going to give you the actual answers but if you want to attempt it I'll be happy to critique your work.
    Unknown008's Avatar
    Unknown008 Posts: 8,076, Reputation: 723
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    #3

    Aug 16, 2009, 10:45 AM

    Mutually exclusive means that one cannot happen of the other happens. For example, if you toss a coin, you either have a head or a tail, not both.

    1. The probability that either of the events occur = sum of probability.

    2. The probability that neither events occur = Take the probability that either of the events occur from 1.
    s_cianci's Avatar
    s_cianci Posts: 5,472, Reputation: 760
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    #4

    Aug 16, 2009, 10:51 AM
    Quote Originally Posted by Unknown008 View Post
    Mutually exclusive means that one cannot happen of the other happens. For example, if you toss a coin, you either have a head or a tail, not both.

    1. The probability that either of the events occur = sum of probability.

    2. The probability that neither events occur = Take the probability that either of the events occur from 1.
    Here you've been told how to do it, so go for it!
    patsygee1's Avatar
    patsygee1 Posts: 3, Reputation: 1
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    #5

    Aug 16, 2009, 10:55 AM

    P(X or Y) = P(X) + P(Y)
    P(X or Y) = .05 + .02 = .07 is the probability of x or y occurring
    P(X or Y) = P(X) + P(Y) -1
    P(X or Y) = .05 + .02 -1
    P(X or Y) = -.93 probability neither x nor y will happen
    Unknown008's Avatar
    Unknown008 Posts: 8,076, Reputation: 723
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    #6

    Aug 16, 2009, 10:59 AM

    The first one is correct.

    However, the second one is not. You take 0.07 from 1, that is 1-0.07 and not the other way round. Probability is never negative. Probability ranges from 0 to 1 only.
    s_cianci's Avatar
    s_cianci Posts: 5,472, Reputation: 760
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    #7

    Aug 16, 2009, 11:01 AM
    Quote Originally Posted by Unknown008 View Post
    The first one is correct.

    However, the second one is not. You take 0.07 from 1, that is 1-0.07 and not the other way round. Probability is never negative. Probability ranges from 0 to 1 only.
    You got it!
    patsygee1's Avatar
    patsygee1 Posts: 3, Reputation: 1
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    #8

    Aug 16, 2009, 11:08 AM

    Thanks for your help. Look forward to collaborating with you again
    Unknown008's Avatar
    Unknown008 Posts: 8,076, Reputation: 723
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    #9

    Aug 16, 2009, 11:11 AM

    You're most welcomed! :)
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