Suppose that A and B are independent events such that =PA0.20 and =PB0.30.Find P∩AB and P∪AB. (If necessary, consult a list of formulas.)(a) =P∩AB(b) =P∪AB
Question
Suppose that A and B are independent events such that =PA0.20 and =PB0.30. Find P∩AB and P∪AB. (If necessary, consult a list of formulas.)
(a) =P∩AB
(b) =P∪AB
Solution
To find P∩AB, we need to use the formula for the intersection of two independent events. The formula is P∩AB = P(A) * P(B). Given that P(A) = 0.20 and P(B) = 0.30, we can substitute these values into the formula:
P∩AB = 0.20 * 0.30 = 0.06
Therefore, P∩AB = 0.06.
To find P∪AB, we need to use the formula for the union of two independent events. The formula is P∪AB = P(A) + P(B) - P∩AB. Again, substituting the given values:
P∪AB = 0.20 + 0.30 - 0.06 = 0.44
Therefore, P∪AB = 0.44.
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