## What Percentage of US Teachers are Millionaires?

I saw a Statistic that said 14% of the millionaires in US are teachers, second only to managers and ahead of lawyers and doctors.

Given this and what you know about teachers, what percentage of teachers do you think are millionaires?

About same? Higher? Lower? Write down the first thought that comes to your mind.

My preconceived notion, based on what I can selectively recall, is there are far fewer millionaires among teachers compared to rest of population. In other words, while 14% of the millionaires are teachers, far fewer proportion of teachers are millionaires.

Until I did the math.

P( Teacher | Millionaire) = P( T | M ) = 0.14

What we want is given someone is a teacher, how likely is that teacher a millionaire, that is  what is P(M | T).

P(M | T) = P(T | M)  X P(M) / P(T)

To compute this we need

1. What proportion of US population are teachers , P(T)
2. What proportion of US population are millionaires, P(M)

Data from US Census says, there are 7.2 million teachers and 8.6 million people are millionaires.

That means P (M | T) is 16.8%, or one in six teacher is a millionaire.