Wk1 Lab 2 Monty hall possible math error or typo and a missing variable definition

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|ğ‘ ğ‘¤ğ‘–ğ‘¡ğ‘â„Ž)=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

Hi @Kevin_Shey!

You are correct, there should be P(E3) = 0.

Regarding the k. It is being defined when we describe the problem, but it is not present in the Analytic Solution section. We will add a formal definition in this section. Thanks for flagging this!

Thanks,
Lucas