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The accompanying Venn diagram shows thre...

The accompanying Venn diagram shows three events, A, B and C and also the probabilities of the various intersections `["for instance", P (AcupB)=0.7].` Determine
(i) P (A)
(ii) `P (Bcapoverset(-)C)`
(iii) `P (AcupB)`
(iv) `P (Acapoverset(-)B)`
(v) `P (BcapC)`
(vi) Probability of exactly one of the three occurs.

Text Solution

AI Generated Solution

To solve the problem step by step, we will use the information provided in the Venn diagram and the given probabilities. Let's denote the probabilities of the intersections and unions as follows: - Let \( P(A \cap B) = 0.07 \) - Let \( P(A \cup B) = 0.7 \) - Let \( P(B \cap C) = 0.15 \) - Let \( P(A \cap C) = 0.10 \) - Let \( P(B) = 0.20 \) ...
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