Question

Let A and B be events such that P (A) = 0.7, P (B) = 0.6 and P (AUB) = 0.8. Find P (A∩B) and P (A’∩B).  

Answer 1

$$P(A\cup B)=P(A)+P(B)-P(A\cap B)$$

$$P(A\cap B)=P(A)+P(B)-P(A\cup B)$$

i)

$$P(A\cap B)=0.7+0.6-0.8=0.5$$

ii)

$$P(A'\cap B)=P(B)-P(A\cap B)=0.6-0.5=0.1$$