Question

If two events A and B are such that P(A') =0.3, P(B)=0.4 and P(A∩B′)=0.5, then P(B/AUB)=

Answer 1

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