2. Explain the Monte Hall Paradox with a Contingency Table. The Monte Hall Paradox comes from the Morning Game Show "Let's Make a Deal" which used to be shown right before the "Price is Right" 5 days a week. Monte Hall was the name of the Host. For the final deal there are 3 doors labeled, Door #1, Door #2, and Door #3 (yes that is what they were called). One of the three doors was a Grand Prize and behind the other two doors was nothing. The Contestant would pick one of the doors, for the purpose of this problem (let's say they picked Door #1). Then Monte Hall would open one of the losing doors, (let's say Door #2 just to keep it simple). Now the Contestant has a choice, they can stay with their choice (in our Example Door #1) or change to the remaining door (in this case Door #3). The Paradox is that the remaining door (in our example Door # 3) actually is the door with the Grand Prize 2/3 of the time. Explain why it's not 1/2.

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2. Explain the Monte Hall Paradox with a
Contingency Table.
The Monte Hall Paradox comes from the Morning Game Show "Let's Make a Deal" which
used to be shown right before the "Price is Right" 5 days a week. Monte Hall was the
name of the Host. For the final deal there are 3 doors labeled, Door #1, Door #2, and
Door #3 (yes that is what they were called). One of the three doors was a Grand Prize
and behind the other two doors was nothing. The Contestant would pick one of the
doors, for the purpose of this problem (let's say they picked Door #1). Then Monte Hall
would open one of the losing doors, (let's say Door #2 just to keep it simple). Now the
Contestant has a choice, they can stay with their choice (in our Example Door #1) or
change to the remaining door (in this case Door #3). The Paradox is that the remaining
door (in our example Door #3) actually is the door with the Grand Prize 2/3 of the time.
Explain why it's not 1/2.
Transcribed Image Text:2. Explain the Monte Hall Paradox with a Contingency Table. The Monte Hall Paradox comes from the Morning Game Show "Let's Make a Deal" which used to be shown right before the "Price is Right" 5 days a week. Monte Hall was the name of the Host. For the final deal there are 3 doors labeled, Door #1, Door #2, and Door #3 (yes that is what they were called). One of the three doors was a Grand Prize and behind the other two doors was nothing. The Contestant would pick one of the doors, for the purpose of this problem (let's say they picked Door #1). Then Monte Hall would open one of the losing doors, (let's say Door #2 just to keep it simple). Now the Contestant has a choice, they can stay with their choice (in our Example Door #1) or change to the remaining door (in this case Door #3). The Paradox is that the remaining door (in our example Door #3) actually is the door with the Grand Prize 2/3 of the time. Explain why it's not 1/2.
Expert Solution
Step 1

So as we know that the monte hall paradox has three doors. One of which has a grand prize. The contestant is supposed to choose a door. Then the host of the show will always open one door from the remaining two doors, which does not have the prize. Then the contestants are free to switch their selection to the door remaining or stick to their first choice.

Here we have to explain the paradox with a contingency table.

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