# Bayes Theorem - Validating Questionable Results

Supposed we have a large data set regarding a users Credit History (1-Good, 0-Bad) and whether or not their Loan (1-Yes, 0-No) has been approved.

The probabilities are calculated and they look like this:

|---------------------|------------------|------------------|
|                     |        Yes       |       No         |
|---------------------|------------------|------------------|
|    Loan Approved?   |         68%      |       32%        |
|---------------------|------------------|------------------|
|    Good Credit?     |         84%      |       16%        |
|---------------------|------------------|------------------|


And we apply Bayes' Theorem:

P(Approved|Good Credit) = (0.68)(0.84) / [(0.68)(0.84) + (0.32)(0.16)] = 91.77%

Great! That seems to make sense.

But now...

P(Denied|Good Credit) = (0.32)(0.84) / [(0.32)(0.84) + (0.68)(0.16)] = 71.18%

This cannot be correct but I'm not sure how to validate this outcome (they are mutually exclusive). How does one validate results when they don't seem intuitive (or reasonable)?