Let A and B be two events such that =PA0.07 and =PB0.28.Do not round your responses. (If necessary, consult a list of formulas.)(a) Determine P∪AB, given that A and B are mutually exclusive.(b) Determine P∪AB, given that A and B are independent.
Question
Let A and B be two events such that =PA0.07 and =PB0.28.Do not round your responses. (If necessary, consult a list of formulas.)(a) Determine P∪AB, given that A and B are mutually exclusive.(b) Determine P∪AB, given that A and B are independent.
Solution
(a) To determine P∪AB, given that A and B are mutually exclusive, we can use the formula P(A∪B) = P(A) + P(B). Since A and B are mutually exclusive, they cannot occur at the same time. Therefore, P(A∩B) = 0.
Given that PA = 0.07 and PB = 0.28, we can substitute these values into the formula:
P(A∪B) = P(A) + P(B) - P(A∩B) = 0.07 + 0.28 - 0 = 0.35
Therefore, P∪AB = 0.35.
(b) To determine P∪AB, given that A and B are independent, we can use the formula P(A∪B) = P(A) + P(B) - P(A∩B).
Since A and B are independent, the occurrence of one event does not affect the probability of the other event. Therefore, P(A∩B) = P(A) * P(B).
Given that PA = 0.07 and PB = 0.28, we can substitute these values into the formula:
P(A∪B) = P(A) + P(B) - P(A∩B) = 0.07 + 0.28 - (0.07 * 0.28) = 0.07 + 0.28 - 0.0196 = 0.3304
Therefore, P∪AB = 0.3304.
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