Question 515540
The inclusion-exclusion principle tells us that:

P(A or B) = P(A) + P(B) - P(A and B)

We subtract P(A and B) because A and B is included in both A and B, so by just taking P(A) + P(B), you are double-counting the overlap P(A and B).

We know that P(A or B) = 0.5, P(A) = 0.2, and P(B) = 0.7.  We substitute these values into the formula above and solve for P(A and B).

0.5 = 0.2 + 0.7 - P(A and B)
0.5 = 0.9 - P(A and B) (simplify)
-0.4 = -P(A and B) (subtract 0.9 from both sides)
0.4 = P(A and B) (negate both sides)

So P(A and B) = 0.4.