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Math Help - Probabilty with events

  1. #1
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    Exclamation Probabilty with events

    We did this ages ago and I really can't remember how to do it! You will be loved forever if you can help me with this!

    Question

    The events A and B are such that

    P(A) = 5/16, P(B) = 1/2 and P(A|B) =1/4

    Find
    (a) P(AnB)
    (b) P(B'|A)
    (c) P(A'uB)
    (d) Determine, with reason, whether or not the events A and B are independant.

    I know it's probably the easiest thing ever but I really can't remember what to do

    Thanks in advance!
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  2. #2
    Junior Member frenzy's Avatar
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    Quote Originally Posted by jonannekeke View Post
    We did this ages ago and I really can't remember how to do it! You will be loved forever if you can help me with this!

    Question

    The events A and B are such that

    P(A) = 5/16, P(B) = 1/2 and P(A|B) =1/4

    Find
    (a) P(AnB)
    (b) P(B'|A)
    (c) P(A'uB)
    (d) Determine, with reason, whether or not the events A and B are independant.

    I know it's probably the easiest thing ever but I really can't remember what to do

    Thanks in advance!
    Do you know the definition for conditional probability?

    P(A|B)=\frac{P(A\cap B)}{P(B)}

    or using the notation you used

    P(A|B)=P(AnB)/P(B)


    provided P(B)>0


    (Hopefully this site will get latex back soon)
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  3. #3
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    I'm sorry, I don't understand I don't know why but I really can't remember any of this probability stuff, how do you actually work out P(AnB)? I'm so confused
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  4. #4
    Junior Member frenzy's Avatar
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    P(A|B)=P(AnB)/P(B)

    using the above in the form


    P(AnB) =P(A|B)P(B)

    =1/4*1/2=1/8

    ---------

    P(B'|A)=1-P(B|A)

    =1-P(BnA)/P(A)=1-P(A|B)*P(B)/P(A)

    =1-1/4*(1/2)/(5/16)
    =1-1/4*1/2*(16/5)
    =1-2/5=3/5

    ---------

    Can you figure out the rest?
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  5. #5
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    I'm not sure

    Has part (c) got something to do with 1- P(A) or am I completely wrong?
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  6. #6
    Junior Member frenzy's Avatar
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    P(A'uB)=1-P(AnB')

    =1-P(B'|A)*P(A)

    =...
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  7. #7
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    ... so would that be

    1-(3/5)*(5/16)?
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  8. #8
    Junior Member frenzy's Avatar
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    Quote Originally Posted by jonannekeke View Post
    ... so would that be

    1-(3/5)*(5/16)?
    yes
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  9. #9
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    Yay at least I did one bit, kinda

    I don't get part (d) though...
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  10. #10
    Junior Member frenzy's Avatar
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    Quote Originally Posted by jonannekeke View Post
    Yay at least I did one bit, kinda

    I don't get part (d) though...
    Two events are independent if knowing that one occurs tells you nothing about whether the other occurs.

    for your problem

    P(A) = 5/16 and P(A|B) =1/4

    if A and B were independent then P(A|B)=P(A)

    since they are different the two events are not independent
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  11. #11
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    Thank you sooooo much!
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