Question 1027191
Let x = P(A) and y = P(B).
Then from the addition law of probability, 

0.9 = x+y - 0.4 ==> x+y = 1.3
Also, since A, B are independent events, P(A∩B) = P(A)P(B) = xy = 0.4

==> x(1.3 - x) = 0.4, or {{{x^2 - 1.3x +0.4 = 0}}}

Directly using the quadratic formula, we get the solutions x = 0.8, 0.5.

Since x > y, it follows that P(A) = 0.8 and P(B) = 0.5.