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The probability that at least one of the events A or B occurs is equal to the sum of probabilities P(A) + P(B) minus
the probability that BOTH events (A & B) occurs at the same time:
P( at least one of the events A or B occurs ) = P(A) + P(B) - P(A & B).
Since the events A and B are independent, P(A & B) = P(A)*P(B) = 0.3*0.4 = 0.12, so the probability
that at least one of the two events will happen is
P( at least one of the two events will happens ) = P(A) + P(B) - P(A)*P(B) = 0.3 + 0.4 - 0.3*0.4 = 0.58.
From this, we should subtract the probability that BOTH events (A & B) occur.
So, the final answer to the problem question is
P( exactly one of the events A or B occurs ) = P(A) + P(B) - 2P(A & B) = 0.58 - 0.12 = 0.46. ANSWER
Another way to derive the same formula and to get the same answer is THIS :
the value P(A) - P(A & B) is the probability that only A will occur with no B;
the value P(B) - P(A & B) is the probability that only B will occur with no A.
Therefore, the sum P(A) + P(B) - 2*P(A & B) is the probability under the question.
