Re: probability question
Suppose that c and b U e are mutually exclusive, with P(c) = 0.4 and P(b U e) = 0.6. a and d only happen if c happens and P(a U d) = 0.2. That satisfies all four expressions and allows Pa(a) to take any value between 0 and 0.2.
We know P(a) can't be greater than 0.2 because then the first and last expressions conflict. So 0 <= P(a) <= 0.2.
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