How do u proof these?

  1. 1. Prove each of the following statements (assume that any conditioning event has positive probability).
    (a) If A is subset of B then P(B|A)=1 and p(A|B)=P(A)/P(B).
    (b) If A and B are mutually exclusive, then p(A|A u B)=((P(A)/((P(A)+P
    (B))
    (C) P(A n B n C)= P(A|B n C) P( B|C) P(C)

    I"m really having problem in doing these. could someone help me out?
     
  2. jcsd
  3. matt grime

    matt grime 9,396
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    You just need to use the rules/identities of probability:

    P(X|Y) = P(XnY)/P(Y)

    and if A < B, then P(AnB)= P(A) since AnB=A, and P(AuB)=P(B) since AuB=B

    if A and B are mutually exclusive then P(AnB)=0 and P(AuB)=P(A)+P(B)

    the third follows from repeatedly applying the formula for conditional probability.
     
  4. Moderator's note: please don't do others' homework for them
     
    Last edited by a moderator: Aug 23, 2004
  5. Hurkyl

    Hurkyl 16,090
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    Have you been able to get anywhere on this, Altemicione?
     
  6. Moderator's note: Same goes for you
     
    Last edited by a moderator: Aug 30, 2004
  7. Why can't we help a brother out?
     
  8. matt grime

    matt grime 9,396
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    Homework Helper

    you can, but just feeding the answers helps no one.
     
  9. helps him pass his class
    so it helps one person
    then it helps his parents so they have to pay less for when he goes to college if he is still in high school
    so then the fincacial benefits spread through is family
    so in the end it could help a lot of people

    plus he prob learn how to do in class tomorrow
    but if u dont' have hw u get 0
     
  10. Gokul43201

    Gokul43201 11,141
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    You think feeding him homework solutions makes him a better student and improves his odds of scoring higher in SATs (or whatever) ?
     
  11. "If someone is hungry, don't give him a fish : teach him to fish !"
    who said that ?
     
  12. matt grime

    matt grime 9,396
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    Probably Gandhi
     
  13. HallsofIvy

    HallsofIvy 40,229
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    "If you give a man a fish, he will eat for a day. If you teach a man to fish, he will never work another day in his life!"
     
  14. Galileo

    Galileo 2,002
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    Homework Helper

    Or:

    If you give a man a fish he will eat for a day. If you teach a man to fish he will drink beer, tell lies and wear a stupid hat.
     
  15. Thanks you all for answering my "off-topic" question ! (although Galileo's version looks suspicous to me (^_^)
     
  16. Gokul43201

    Gokul43201 11,141
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    You mean 'fishy' ?
     
  17. Sorry, I am not too sure about what fishy could mean ...
     
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