If A and B are independent and P(A) =P(B|A) =.4, What is P(A∪B) =?
To find the probability of the union A∪B, we need to apply the formula:
P(A∪B) = P(A) + P(B) - P(A∩B)
However, since A and B are independent events, we know that P(A∩B) = P(A) * P(B). Therefore, we can rewrite the formula as:
P(A∪B) = P(A) + P(B) - P(A) * P(B)
Given that P(A) = P(B|A) = 0.4, we can substitute these values into the formula:
P(A∪B) = 0.4 + P(B) - 0.4 * P(B)
Since A and B are independent, P(B) = P(B|A) = P(B|A') = P(B), where A' represents the complement of A. So we can substitute P(B) with 0.4:
P(A∪B) = 0.4 + 0.4 - 0.4 * 0.4
Now we can calculate this value:
P(A∪B) = 0.4 + 0.4 - 0.16
P(A∪B) = 0.8 - 0.16
P(A∪B) = 0.64
Therefore, the probability of the union A∪B is 0.64.