Assume that Pr[A] = 0.4, Pr[B] = 0.7, and Pr[A nB] = 0.3.

Question

events A and B in a sample space S. Assume that Pr[A] = 0.4, Pr[B] = 0.7, and Pr[A ∩B] = 0.3.
(1) Pr[B′∩A] =

(2) Pr[A′∩B] =

(3) Pr[A′∩B′] =

Answer 1

PA=.4, PB = .7 PA^B = .3. draw a Venn diagram P~B = .4+.7 -.3=.8-.7 = .1

PA^~B = .1 = 1/10 = 10% chance

P~A^B = .3 = 3/10 = 30%

Pr-A^~B = .2 = 1/5 = 20%