Conditional Probability?

Question

I have looked this over countless times, but can't figure it out. Any help would be greatly appreciated.

Two events A and B are such that P(A)=3/4, P(B/A)=1/5 and P(B'/A')=4/7

By use of tree diagram or otherwise, find

a) P (A and B) (already found it to be 3/20)

b) P (B) (this is the one i'm stuck on)

Seriously any HELP AT ALL WOULD BE GREATLY APPRECIATED!

thanks in advance...

ps: where I say (B/A) i don't mean B divided by A) but B happens given that A has happened

Answer 1

P(B) = P(A)P(B | A) + P(A')P(B | A')
= P(A)P(B | A) + (1-P(A))(1 - P(B' | A'))
= (3/4)(1/5) + (1/4)(1 - 4/7)
= 3/20 + 3/28
= 21/140 + 15/140
= 36/140
= 9/35.