I am currently working through “Think Bayes: Bayesian Statistics in Python”
05-18-2021 edition
In Chapter 2, p.24, there is given data, and then a bulleted list of hypotheses and their probability given the data.
The bulleted list is only correct if the contestant has chosen door 1. This assumption is not stated clearly within this section that lays out hypotheses, data, and making it very confusing for a student, especially one not familiar with the Monty Hall Problem.
The text would be better written to reiterate here that door one has been chosen before Monty opens door 3. The probabilities are dependent on which door the contestant has chosen. Unless explicitly stated, the probabilities are actually different than the bulleted list.
For example:
If the contestant did not choose a door at all, but Monty still opened door 3 to a goat (which while against the rules is also possible - chaotic good here) , the probability that the car would be behind door 2 given the data, would be 50% instead of 100% when the contestant chooses door 1.
Thanks for your time. Writing and editing math textbooks is no easy feat!
Regards,
Betsy