Here is the depiction of the sample space of a probabilistic model, where the reals \(x,y,z,t > 0\) indicate the probability mass of the corresponding regions. Note that they are not probabilities themselves, they are only proportional to the probabilities of the corresponding events.

Conditional Venn

Indicate the following probabilities in terms of \(x,y,z,t\):

  1. \(P(A\given B) =\)
  2. \(P(A\given \neg B) =\)
  3. \(P(A\cap \neg B) =\)
  4. \(P(B\given A\cap B) =\)
  5. \(P(A\cup B) =\)

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