Final answer:
To find P(B/A∪B), we can use the formula for conditional probability. Given P(A') = 0.3, P(B) = 0.4, and P(A∩B') = 0.5, we can substitute these values into the formulas and calculate P(B/A∪B) as 3/7.
Step-by-step explanation:
To find P(B/A∪B), we can use the formula for conditional probability:
P(B/A∪B) = P(A∪B) * P(B/A)
Since A and B are events, the formula for the union of two events is:
P(A∪B) = P(A) + P(B) - P(A∩B)
Given P(A') = 0.3, we know that P(A) = 1 - P(A') = 1 - 0.3 = 0.7. And we are given P(B) = 0.4. Finally, P(A∩B') = 0.5.
Now we can substitute these values into the formulas:
P(A∪B) = 0.7 + 0.4 - 0.5 = 0.6
P(B/A) = P(B∩A) / P(A)
Since we are given P(A∩B') = 0.5, we know that P(B∩A) = 1 - P(A∩B') = 1 - 0.5 = 0.5
Substituting these values into the formula:
P(B/A) = 0.5 / 0.7 = 5/7
Now we can calculate P(B/A∪B) using the formula for conditional probability:
P(B/A∪B) = P(A∪B) * P(B/A) = 0.6 * (5/7) = 3/7