If you randomly select an adult, then you are more likely to select a person that has earned an advanced degree than a person who is teaching (since there are a lot less tenchers than people with an advanced degree).

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)

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)