Question 1105791
p( neither happens ) = 1 - p( either E1 or E2 happens )
p ( neither happens ) = (1-p1)*(1-p2) = 1 - p1 - p2 + p1p2

[ p1p2 = p12 as defined in problem statement ]

1 - p( either E1 or E2 happens ) = 1 - p1 - p2 + p12
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Solving for p ( either E1 or E2 ):
p( either E1 or E2 happens ) = 1 - (1 - p1 - p2 + p12) = {{{ highlight(p1 + p2 - p12) }}}