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    Im really puzzled about this question: Suppose that A, B and C are events in a sample space S, such that A∪B∪C = S and A∩B∩C= ∅ If P(A) = 0.139, P(B) = 0.268, P(A∩B)= 0.045, P(B∩C)= 0.204 and P(A∩C) = 0.055, find P(C), and P(A|C). If anyone can explain then that will be helpful
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    (Original post by AFraggers)
    Im really puzzled about this question: Suppose that A, B and C are events in a sample space S, such that A∪B∪C = S and A∩B∩C= ∅ If P(A) = 0.139, P(B) = 0.268, P(A∩B)= 0.045, P(B∩C)= 0.204 and P(A∩C) = 0.055, find P(C), and P(A|C). If anyone can explain then that will be helpful
    To find P(C) use inclusion exclusion formula you should have seen:



    To find P(A|C) just use the formula for condition probability that is.

    P(A|C)=P(A n C)/P(C)
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    (Original post by poorform)
    To find P(C) use inclusion exclusion formula you should have seen:



    To find P(A|C) just use the formula for condition probability that is.

    P(A|C)=P(A n C)/P(C)
    I still dont totally understand the formula though. will P[E1 ∪ E2 ∪ E3] just be the sample space???
    Also I guess P[E1∩E2∩E3] can be cancelled out as it is an empty set??
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    (Original post by AFraggers)
    I still dont totally understand the formula though. will P[E1 ∪ E2 ∪ E3] just be the sample space???
    Also I guess P[E1∩E2∩E3] can be cancelled out as it is an empty set??
    Yes you are correct with the cancelling part since the set is empty it has probability 0. Also you are correct that the first set you mentioned is the sample space. So what is the probability of the outcome being in the sample space? Rearrange the equation and sub in.
 
 
 
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