MHB How Should I Start My Probability Question to Get the Best Help?

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To receive the best help with probability questions, users should share their progress, including any work done or initial thoughts. This practice allows helpers to understand where the user is struggling and avoid suggesting solutions that have already been attempted. Providing context enhances the quality of assistance and saves time for both the user and the helper. Engaging with the community in this manner fosters more effective problem-solving. Sharing your progress is essential for optimal support in tackling probability challenges.
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Hello Marcus Cheng and welcome to MHB! :D

We ask that our users show their progress (work thus far or thoughts on how to begin) when posting questions. This way our helpers can see where you are stuck or may be going astray and will be able to post the best help possible without potentially making a suggestion which you have already tried, which would waste your time and that of the helper.

Can you post what you have done so far?
 
There is a nice little variation of the problem. The host says, after you have chosen the door, that you can change your guess, but to sweeten the deal, he says you can choose the two other doors, if you wish. This proposition is a no brainer, however before you are quick enough to accept it, the host opens one of the two doors and it is empty. In this version you really want to change your pick, but at the same time ask yourself is the host impartial and does that change anything. The host...

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