2. Conditional probability The Venn diagram below depicts a sample space (S) where the dots are outcomes and the A, B and C subsets are events. Red outcomes are twice as likely than the black outcomes. Calculate the below probabilities. a) [5 pts] P(A | C) = b) [5 pts] P(B | (A ? C)) = c) [5 pts] P(C ? B | ?) =
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A sample space contains six sample points and events A, B, and C as shown in the Venn diagram. The probabilities of the sample points are P(1) = 0.2, P(2) = 0.35, P(3) = 0.05, P(4) = 0.1, P(5) = 0.05, P(6) = 0.25. Use the Venn diagram and the probabilities of the sample points to find: (a) P(C), (b) P(A|C), (c) P(A|B).
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In the Venn diagram shown at the left, $P(A \text { or } B \text { or } C$ ) is represented by the blue areas. In Exercises 28 and $29,$ find $P(A \text { or } B \text { or } C).$ $P(A)=0.40, P(B)=0.10, P(C)=0.50$ $P(A \text { and } B)=0.05, P(A \text { and } C)=0.25, P(B \text { and } C)=0.10$ $P(A \text { and } B \text { and } C)=0.03$
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