Given P(A)=3/4, P(B|A)= 1/5 and P(B'|A')=4/7, find P(B).
from
P(B/A) = p(AnB)/P(A)
P(AnB) =1/5 * 3/4
P(AnB)= 3/20
but
P(A) + P(A') = 1
P(A') = 1 - 3/4
P(A')=1/4
Also
p(A'nB') = P(B'/A') * P(A')
=4/7 * 1/4
P(A'nB')=1/7
P(A'nB') + P(AUB) = 1
P(AUB) = 1 - 1/7
P(AUB)=1/6
P(AUB) = P(A) + P(B) - P(AnB)
P(B) = 1/6 + 3/20 - 3/4
P(B) = 9/35