You notice, I presume, that saying "Afails" and "Bfailsis really no different from saying "A succeeds" and "B succeeds"?

In any case imagine 100 incidents. In 20 of those A fails, and in 15 ofthoseB also fails. In 15 B fails and A does not. So there are 15+ 15= 30 incidents which B fails and in 15 of those A fails. The probability that A will failgiventhat B fails, is 15/30= 1/2= 0.50.

There are 20 incidents in which A fails and in 15 of those B also fails so there are 20- 15= 5 in which A fails but B does not. The probability that A fails and B does not is 5/20= 1/4= 0.25.

(P(B does not fail given that A fails) is NOT equal to 1-P(A and B both fail). 1- P(A and B) is the probability that at least one of A and B fail and that includes "Both A and B fail" as well as "B fails and A does not".