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Assignment 1
Hi,
in 1.2.3. G2 is defined as: Monty shows you a goat behind door No. 2, after we have chosen door No. 1.
Is G2 (and G3) in the tasks 4., 5. and 6. also “Monty shows you a goat behind door No. 2 (3), after we have chosen door No. 1” or only “Monty shows you a goat behind door No. 2 (3)”?
Hi!
Good question! The Gis (goat behind door i) in 4., 5., and 6. are supposed to be the same format (up to i) as the one from 3., so, the probabilities after you have picked door 1. However, it should be easy to convince yourself, given some pretty reasonable fairness assumptions, that they are actually independent of picking the door.
Cheers,
Katja
Hi,
your reply kind of confused me.
So is Gi
a) „Goat behind door i“ or is it
b) „Monty shows me goat behind i after I picked door 1 (As it is stated in 3.)“?
If it is b), then it is not independent from picking the door, because monty would not show me a goat behind the door I picked.
I hope you can comprehend my confusion and provide some clarification.
You are of course correct. I’ve been trying to figure out what I meant by independent, since it made perfect sense to me then. Unfortunately, I can’t quite figure out where the glitch was. Serves me right for bringing up the Monty Hall problem 
So as is stated in the problem, G2 is the probability that Monty shows you a goat behind door number 2, after you have chosen door number 1.
The probability of there being a goat behind door number 2 is of course 2/3. This is not the same G2.
In the following tasks 4. to 6. G2 follows the same definition, that is, Monty shows you a goat behind door number 2, after you have chosen door number 1, and similar for G3.