Let A and B be events in the sample space S, and let P[A]=.41, P[B]=.32 and LaTeX: P\left[B'\cap A\right]=.21. Find LaTeX: P\left[A'\cap B\right]

P(A' ∩ B) = 0.12

Step-by-step explanation:

Given:

P(A) = 0.41, P(B) = 0.32 and P(B' ∩ A) = 0.21

To Find:

P(A' ∩ B)

Solution:

Since, P(B' ∩ A) = P(A) - P(A ∩ B)

By substituting the values given,

0.21 = 0.41 - P(A ∩ B)

P(A ∩ B) = 0.41 - 0.21

              = 0.20

Since, P(A' ∩ B) = P(B) - P(A ∩ B)

P(A' ∩ B) = 0.32 - 0.20

               = 0.12

Therefore, P(A' ∩ B) = 0.12 is the answer.