Assume that P(A) = 0.4, P(B) = 0.4, and P(A∪B) = 0.7. Find P(A∩B) and P(A complement ∩ B complement).
Recall:
P(A∪B) = P(A) + P(B) - P(A∩B)
do we already given 3 of the unknown for this expression to find P(A∩B) ?
To find the probability of the intersection, P(A∩B), you can use the formula:
P(A∩B) = P(A) + P(B) - P(A∪B)
Given that P(A) = 0.4, P(B) = 0.4, and P(A∪B) = 0.7, you can substitute these values into the formula:
P(A∩B) = 0.4 + 0.4 - 0.7
P(A∩B) = 0.8 - 0.7
P(A∩B) = 0.1
Therefore, P(A∩B) = 0.1.
To find the probability of the intersection of the complements, P(A complement ∩ B complement), you can use the formula:
P(A complement ∩ B complement) = 1 - P(A∪B)
Given that P(A∪B) = 0.7, you can substitute this value into the formula:
P(A complement ∩ B complement) = 1 - 0.7
P(A complement ∩ B complement) = 0.3
Therefore, P(A complement ∩ B complement) = 0.3.