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Question: create a venn diagram showing three sets abc such that...

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Create a Venn diagram showing three sets A,B,C, such that neither of them is a subset of the others. A and B intersect. C intersects with both A and B such that C doesn’t intersect with A without B , however C intersects with B without A.

(a) Shade on your Venn diagram the event (B ∪ C) ∩ Ac

(b) Find the expression for the probability of the event from part (a) in terms of probabilities of A, B, C and their intersections as necessary. (The expression should not depend on probabilities of complementary events).

(c) Determine the value of probability from part (b) if P (A) = 0.45, P (A ∪ B) = 0.75, P(A∩B)=0.3, P(A∪C)=0.85, P(A∩B∩C)=P(A∩C)=0.1, P(B∩C)=0.4

(Hint: To find P(C) and/or P(B) if necessary, use Addition Law of probability).

 

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