Hi Everyone,
I just want to double-check if I am reading this wrong in the Monty Hall lab:
From the problem statement:
Now you are mostly done, because as you know, 23=𝑃(𝐸2∪𝐸3)=𝑃(𝐸2)+𝑃(𝐸3)−𝑃(𝐸2∩𝐸3)
You already know that 𝑃(𝐸2∩𝐸3)=0, because they are mutually exclusive events (the car is behind in only one of the three doors),
and the Host gave you a very important piece of additional information:
𝑃(𝐸2)=0.
With this, you can easily conclude that:
𝑃(𝑤𝑖𝑛|𝑠𝑤𝑖𝑡𝑐ℎ)=𝑃(𝐸2)=2/3.
As you can notice:
The explanation said -----> P(E2) = 0.
And then stated that P(E2) = 2/3
I assume the explanation meant to state P(E3) = 0, NOT P(E2) = 0.
Am I reading this wrong?
Issue 2:
In Monty Hall 5.2 Analytic Solution:
The following was stated by the explanation:
"Note that, since the Host never opens the same door the player chose and also never opens the winning door, there is an upper bound for 𝑘 , which is 𝑛−2, so
0≤𝑘≤𝑛−2."
The definition of “k” was never defined when the variable was introduced.
I try to infer “k” meaning, but I was a bit confused.
Please clarify “k” definition.
Thanks,
Kevin