Question

What is wrong with the expression upper p left parenthesis upper a right parenthesis plus upper p left parenthesis upper a overbar right parenthesis equals 0.5p(a)+pa=0.5​?

Answer 1

P(A) is the probability of happening A
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P( A ) is the probability of not happening A.
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Evidently, A and A represents the total universe: either A happens or A not happens.
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So, P(A) + P( A ) has to be 1, not 0.5.