SOLUTION: Suppose that E and A are events in the sample space S. Suppose P(E|A)= 1/3 and P(E|A')=1/3. Is it necessarily true that P(E)=1/3? If yes, justify algebraically. If no, find sample
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Question 1029575: Suppose that E and A are events in the sample space S. Suppose P(E|A)= 1/3 and P(E|A')=1/3. Is it necessarily true that P(E)=1/3? If yes, justify algebraically. If no, find sample space S and events A and E that satisfy P(E|A)= 1/3 and P(E|A')=1/3 and P(E) =/= 1/3.
Answer by richard1234(7193) (Show Source): You can put this solution on YOUR website!
Yes -  = P(E \mid A) \cdot P(A) + P(E \mid \overline{A}) \cdot P(\overline{A}))
. Using the given facts, this simplifies to  = \frac{1}{3} \cdot P(A) + \frac{1}{3} \cdot P(\overline{A}) = \frac{1}{3} \cdot (P(A) + P(\overline{A}) = \frac{1}{3})
.
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