99% of all babies survive delivery. However, 10 % of all births involve Cesarean (C) sections, and when a C section is performed the baby survives 98% of the time. If a randomly chosen pregnant woman does not have a C section, what is the probability that her baby survives?
P(E) = 1 - P(EC)
P(E U F) = P(E)+P(F)-P(EF)
The Attempt at a Solution
P(S) = .99 for baby survival
P(C) = .1 for C section
P(S|C) = .98 for babies surviving the C section
P(S|CC) = ??
So I tried P(S|CC) =P(SCC)/P(CC)
I know the dominator = .9. I tried solving for the numerator using:
P(SCC)= P(S)+P(C)-P(S U C), but at this point, I don't know what the P(S U C) is.