Question 1024793
P(E|F) = P(E∩F)/P(F) ==>P(F) = (4/3)P(E ∩ F)
P(F|E) = P(E∩F)/P(E) ==>P(E) = 2P(E ∩ F)

==> P(E U F) = P(E) + P(F) - P(E ∩F) = 2P(E ∩ F) +  (4/3)P(E ∩ F) - P(E ∩F) = (7/3)P(E ∩F)

==> 2/3 = (7/3)P(E ∩F)

==> 2 = 7P(E ∩F), or

P(E ∩F) = 2/7.

==> P(E) = 2P(E ∩ F) = 4/7, and 

==> P(F) = (4/3)P(E ∩ F) = 8/21.