Question

p(O)=0.5. Events A and B are conditional independent events given O and ~O respectively, that is, A and B are conditional independent events given O and A and B are also conditional independent events given ~O. We also know that p(A|O)=p(~A|~O)=0.8, p(B|O)=0.75, and p(B|~O)=0.5. Determine p(O|(A∩B)).

Answer 1

To determine p(O|(A∩B)), we can use Bayes' theorem. Bayes' theorem states that p(O|(A∩B)) = (p(A∩B|O) * p(O)) / p(A∩B). To calculate this, we need to find p(A∩B|O) and p(A∩B).

Step-by-step explanation:

To determine p(O|(A∩B)), we can use Bayes' theorem. Bayes' theorem states that p(O|(A∩B)) = (p(A∩B|O) * p(O)) / p(A∩B). To calculate this, we need to find p(A∩B|O) and p(A∩B).

We are given that A and B are conditional independent events given O and ~O, which means p(A|O) = p(A) and p(B|~O) = p(B). Thus, p(A∩B|O) = p(A|O) * p(B|O) = 0.8 * 0.75 = 0.6. Now, to find p(A∩B), we can use the formula p(A∩B) = p(A) * p(B). We are not given p(A), so we cannot calculate p(A∩B).

Answer 2

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Step-by-step explanation: