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Unions and Intersections

  1. Oct 9, 2012 #1
    1. The problem statement, all variables and given/known data
    A and B are independent, P(A) = 0.30, P(B) = 0.50. Compute P(A U B) and P(A' intersect B).



    3. The attempt at a solution
    P(A U B) = 0.30 + 0.50 = 0.80
    P(A' intersect B) = 1 - 0.30 = 0.70
    this is obviously wrong
     
  2. jcsd
  3. Oct 9, 2012 #2

    ehild

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    It is really wrong. What does it mean that A and B are independent? When is it true that P(A U B) = P(A)+P(B)?
    Try to draw the Venn diagram.

    ehild
     
  4. Oct 9, 2012 #3
    Well I got the first one incorrect and I don't know exactly why because wouldn't the union be what is included in the set A and B. That's why I added them.

    For the second on I'm no sure how to really do that one. I just understand it as not in A and in B
     
  5. Oct 9, 2012 #4

    ehild

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  6. Oct 9, 2012 #5

    SammyS

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    Yes, of course you're correct, ehild !

    (I have deleted my earlier post. )
     
  7. Oct 9, 2012 #6

    ehild

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    P(AUB)=P(A)+P(B)-P(A[itex]\cap[/itex]B)
    Look after how to calculate the probability P(A[itex]\cap [/itex]B) if A and B are independent.

    It is the probability that A does not happen and B happens.

    ehild
     
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