P(A) > P(P)
Most of the tenchers have an advanced degree (especially in high schools universities) and thus if you have know that a person is a teacher, then this person is morelikely to have an advanced degree compared to the proportion of people with advanced degrees in the general population.
P(AIT) > P(A)
We expect people with advanced degrees to be more likely to be teachers than people in general (because you need a, degree to be allowed to teach).
P(E|A) > P(E)
Among the population of people with advanced degrees, most of them will not be teachers and we suspect that there will be a smaller proportion of teachers among the population of people with advanced degrees than the proportion of people with advanced degrees. In other words, we will be less likely to select a teacher among those with advanced degrees than we are to select somebody with an advanced degree.
P(A) > P(E|A)
Combining these four inequalities, we then obtain:
P(T) < P(TIA) < P(A) < P(AIT)