[jpiabrantes]

Your denominators are wrong.

The denominator should be the probability of the classifier being positive: P(True Positive)+P(False Positive)

Since you assumed that P(False Positive) = P(False Negative) = (1-P(True Positive))/2 = (1-P(True Negative))/2

In the algorithm case the denominator is 0.8x0.04+0.1x0.96=0.128

In the human case the denominator is 0.6x0.04+0.2x0.96=0.216

In summary, if a human thinks someone is homosexual, the probability increases to 11.1%. If the algorithm makes that call the probability increases to 25%.