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