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Math Help - Mutually exclusive events? need help for sure

  1. #1
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    Question Mutually exclusive events? need help for sure

    P(E_1)=0.25, P(E_2)=0.75, P(FlE_1)=0.05. P(FlE_2)=0.12. P(E_2lF). Ok I'm looking for an area or space between both. As for the text book no good example is close to this one. Ok so 0.25*0.75=.1875, and 0.05*0.12=.006. Now is the hard part what do I do next. I would like to say 0.188 is the answer but I'm not sure. List of possible answers are -

    1. 0.188
    2. 0.878
    3. 0.060
    4.0.370

    Thanks for any help given.
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  2. #2
    Eater of Worlds
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    What do you want to find, P(E_{2}|F)?.
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  3. #3
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    Post opps so sorry about that

    it was P(E_2lF)=___?
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  4. #4
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    Hello, kwtolley!

    I solved it with Bayes' Theorem and a lot of algebra . . .
    . . always a dependable method.


    P(E_1) = 0.25,\;\; P(E_2) = 0.75,\;\; P(F|E_1)  = 0.05,\;\;P(F|E_2) = 0.12

    Find P(E_2|F)

    1)\;0.188\qquad2)\;0.878\qquad3)\; 0.060\qquad4)\;0.370

    Bayes' Theorem: . P(E_2|F) \;= \;\frac{P(E_2\,\land\,F)}{P(F)}


    We are given: . P(F|E_1) = 0.05 . . . This means: . \frac{P(F\,\land\, E_1)}{P(E_1)} \:=\:0.05
    . . Since P(E_1) = 0.25:\;\;\frac{P(F\,\land\,E_1)}{0.25} \:= \:0.05\quad\Rightarrow\quad P(F\,\land\,E_1)\:=\:0.0125<br />

    We are given: . P(F|E_2) = 0.12 . . . This means: . \frac{P(F\,\land\,E_2)}{P(E_2)} = 0.12
    . . Since P(E_2) = 0.75:\;\;\frac{P(F\,\land\,E_2)}{0.75} \:= \:0.12\quad\Rightarrow\quad P(F\,\land\,E_2) = 0.09


    Hence: . P(F)\:=\:P(F\,\land\,E_1) + P(F\,\land\,E_2) \;= \;0.0125 + 0.09 \;= \;0.1025


    Therefore: . P(E_2|F) \;=\;\frac{P(E_2\,\land\,F)}{P(F)}\;=\;\frac{0.09}  {0.1025} \;=\;0.87804878 . . . answer (2)

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  5. #5
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    Smile omg

    Man that was a lot to set up for such a small problem if you ask me. I see the steps now. I got it, I will plug this in for the rest of the problems I have to do. thanks again soooo much for showing me the way.
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