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What is the probability that events A and B both occur?

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sanjib Really wants to Beat The GMAT! Default Avatar
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What is the probability that events A and B both occur? Post Fri Sep 04, 2009 8:11 am
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    What is the probability that events A and B both occur?
    (1) The probability that event A occurs is 0.8.
    (2) The probability that event B occurs is 0.6.
    I think the answer is 1-(both do not occur) so in order to get both do not occur we need both st.1 and st.2.Therefore it should be C.
    But its not the OA. Am I missing something.

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    aakaps Just gettin' started! Default Avatar
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    Post Sat Sep 05, 2009 6:53 pm
    good question!! I just came back from my usual starbucks joint where I solve my practise problems and faced exactly same question.

    So the answer is.....1-both dont occur means....both will NOT occur, together or seperate. Whereas the question is both to occur together.

    So the answer has to be probability of first to occur and then probability of second to occur. Both will multiply. Also you need to check whether the sequence matters. If yes, then multiply by 2, else you have your answer.

    bharathh Really wants to Beat The GMAT! Default Avatar
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    Post Sat Sep 05, 2009 6:58 pm
    I would have gone for C as well.

    I'm guessing it's E because you don't know if A and B are mutually exclusive events... ie. If A occurs B will not occur and vice versa.

    If they are not mutually exclusive, it is not possible to calculate probability.

    sanjib Really wants to Beat The GMAT! Default Avatar
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    Post Sat Sep 05, 2009 10:24 pm
    Please need more explanation.Because the OA is E.

    qwe12 Rising GMAT Star Default Avatar
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    Post Sun Sep 06, 2009 1:27 am
    sanjib wrote:
    What is the probability that events A and B both occur?
    (1) The probability that event A occurs is 0.8.
    (2) The probability that event B occurs is 0.6.
    there are 3 formulas joint probability
    http://en.wikipedia.org/wiki/Probability

    p(a or b) = p(a) + p(b) - p(a and b)

    we do not get p(a and b) from (1), (2) or (1) and (2)

    answer (E)

    Nermal Rising GMAT Star Default Avatar
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    Post Sun Sep 06, 2009 1:44 am
    You can only calculate the probability if you know that the occurence of one event is independent from the occurence of the other event.

    Then you could use formula P(A and B) = P(A)*P(B), it would be 0,8*0,6=0,48 (C)

    But since this fact is not explicitly stated we cannot assume any indepence of the occurence of those events, therefore we don't know:
    Answer E

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