Let A and B be events with P (A) = 0.375; P (B) = 0.5, and. Calculate
1. P(A' ∩ B):
The probability of A complement intersection B can be calculated as follows:
P(A' ∩ B) = P(B) - P(A ∩ B)
P(A ∩ B) = P(A) + P(B) - P(A ∪ B)
P(A' ∩ B) = P(B) - [P(A) + P(B) - P(A ∪ B)]
P(A' ∩ B) = 0.5 - [0.375 + 0.5 - P(A ∪ B)]
P(A' ∩ B) = 0.5 - 0.875 + P(A ∪ B)
P(A' ∩ B) = 0.5 - 0.875 + P(A ∪ B)
P(A' ∩ B) = 0.5 - 0.875 + P(A ∪ B)
P(A' ∩ B) = 0.125 + P(A ∪ B)
2. P(A ∪ B):
Using the formula P(A ∪ B) = P(A) + P(B) - P(A ∩ B), we can calculate:
P(A ∪ B) = 0.375 + 0.5 - P(A ∩ B)
P(A ∪ B) = 0.875 - P(A ∩ B)
Since we do not know P(A ∩ B) directly, we will express P(A ∪ B) using P(A' ∩ B) as calculated in (1):
P(A ∪ B) = 0.125 + P(A' ∩ B)
Therefore, the probabilities of P(A' ∩ B) and P(A ∪ B) are dependent on each other in this scenario.