Let events A and B be such thatP (A ∪ B) = 34, P (A ∩ B) = 14 and P (Ac) = 23.Find P (B) and P (A ∩ Bc)

Sure, I can help with that. Here's how you can find P(B) and P(A ∩ Bc):

Step 1: Find P(B)

We know that P(A ∪ B) = P(A) + P(B) - P(A ∩ B). We can rearrange this formula to solve for P(B):

P(B) = P(A ∪ B) + P(A ∩ B) - P(A)

We know that P(A ∪ B) = 3/4, P(A ∩ B) = 1/4, and P(A) = 1 - P(Ac) = 1 - 2/3 = 1/3. Substituting these values into the formula gives:

P(B) = 3/4 + 1/4 - 1/3 = 1 - 1/3 = 2/3

So, P(B) = 2/3.

Step 2: Find P(A ∩ Bc)

We know that P(A ∩ Bc) = P(A) - P(A ∩ B). We can substitute the known values into this formula:

P(A ∩ Bc) = P(A) - P(A ∩ B) = 1/3 - 1/4 = 1/12

So, P(A ∩ Bc) = 1/12.