# How tall is A?

Here are a series of problems I posed in my Bayesian statistics class:

1) Suppose you meet an adult resident of the U.S. who is 170 cm tall. What is the probability that they are male?

2) Suppose I choose two U.S. residents at random and A is taller than B. How tall is A?

3) In a room of 10 randomly chosen U.S. residents, A is the second tallest. How tall is A? And what is the probability that A is male?

As background: For adult male residents of the US, the mean and standard deviation of height are 178 cm and 7.7 cm. For adult female residents the corresponding stats are 163 cm and 7.3 cm. And 51% of the adult population is female.

If you solve the problems in order, you can reuse code from the first two to solve the third.

Here’s my solution, using a grid algorithm and the libraries from *Think Bayes*:

When I tweeted about this problem, I heard from Colin Carroll, who wrote a solution using PyMC:

And vlad posted a this solution using WebPPL, a browser-based environment for probablistic programming:

You can run that solution at WebPPL.