# Select an adult at random. Let A = person has earned an advanced degree (masters or PhD) and T = person's career is teaching. Rank the following proba

Select an adult at random. Let A = person has earned an advanced degree (masters or PhD) and T = person's career is teaching. Rank the following probabilities from smallest to largest. Justify your answer. P(A)P(T)P(A∣T)P(T∣A)

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Corben Pittman
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)