SOLUTION: The events E1 and E2 are neither independent nor mutually exclusive. Denote by p12 the probability that E1 and E2 both happen. Prove that the probability that at least one of E1 an
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Question 1105791: The events E1 and E2 are neither independent nor mutually exclusive. Denote by p12 the probability that E1 and E2 both happen. Prove that the probability that at least one of E1 and E2happens, is p1+p2-p12.
Answer by math_helper(2461) (Show Source): You can put this solution on YOUR website!
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
—
Solving for p ( either E1 or E2 ):
p( either E1 or E2 happens ) = 1 - (1 - p1 - p2 + p12) =
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