Verifying statement with Bayesian inference

Question

In class we were told we could use Bayesian Inference to verify the following information.

• 99% neonatal deaths in the first four weeks occurs in underdeveloped countries.
  Though around 90% of all births take place in underdeveloped countries, so the chances of a newborn dying is "only" 11 times greater there.

I am not sure how to show this using Bayesian Statistics to verify such statement.

How can we determine this probability without being given survival rates? Thanks

Answer 1

Let $D$ be the event that an infant dies and $U$ be the event that a person is born in an underdeveloped country.

Then $$P(D|U)=\frac{P(U|D)P(D)}{P(U)}$$ and $$P(D|\lnot U)=\frac{P(\lnot U|D)P(D)}{P(\lnot U)}$$

Calculate each one as a multiple of $P(D)$ and compare the results.