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How do i solve this possibility question

  1. Oct 30, 2009 #1
    how do i solve this possibility question

    a scientist does 2 experiments, whose outcomes are independant of each other.

    the possibility of a positive result in experiment A is 0.9
    the possibility of a positive result in experiment B is 0.7

    what is the possibility of a positive outcome in at least one of the experiments?

    what i think i am looking for is P(A∪B) since i want either P(A) or P(B) or P(A∩B)

    the problem is that i dont have enough information,
    the answer is 0.97, which is P(A)+P(B)-P(A)*P(B), but how do i get to this, am i wrong in saying that i am looking for P(A∪B) ? which equation can i use to find this answer?
     
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  3. Oct 30, 2009 #2

    Office_Shredder

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    What is the possibility neither experiment has a positive outcome?

    How does this help you answer the question?
     
  4. Oct 30, 2009 #3
    no not really, how can i find that possibility, i know that it is 1-P(A∪B), but how does that help
     
  5. Oct 30, 2009 #4

    Office_Shredder

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    What is the probability of a negative result for each experiment? Then remember that the experiments are independent, so what is the probability that both A is negative and B is negative in terms of each individual probability
     
  6. Oct 30, 2009 #5
    A negative - 0.1
    B negative - 0.3

    but from here what do i do, can i say that since they are independant P(A∪B)=P(A)+P(B), but that comes to more than 1,
    i see what you are saying, for the negative reult 0.1*0.3, but what rule is this??
     
  7. Oct 30, 2009 #6

    HallsofIvy

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    Assuming A and B are independent, [itex]P(A\cap B)[/itex]= P(A and B)= P(A)P(B).

    [itex]P(A\cup B)[/itex]= P(A or B)= P(A)+ P(B)- [itex]P(A \cap B)[/itex]
    and that is P(A)+ P(B) only if [itex]P(A \cap B)= 0[/itex] (A and B are mutually exclusive) which can't be true if they are independent.
     
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