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Im Stuck????

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

Reply 1

poorform

Original post by AFraggers

To find P(C) use inclusion exclusion formula you should have seen:

$\displaystyle \begin{aligned} (8) \ \ \ \ \ \ P[E_1 \cup E_2 \cup E_3]&=P[E_1]+P[E_1]+P[E_3] \\& \ \ \ \ -P[E_1 \cap E_2]-P[E_1 \cap E_3]-P[E_2 \cap E_3] \\& \ \ \ \ +P[E_1 \cap E_2 \cap E_3] \end{aligned}$

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

P(A|C)=P(A n C)/P(C)

Reply 2

AFraggers

Original post by poorform

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??

Reply 3

poorform

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.