Let’s say you were selected to participate in a TV game show. One of the games y
ID: 3121685 • Letter: L
Question
Let’s say you were selected to participate in a TV game show. One of the games you will be playing is Cash or Nothing; where you are showed three curtains, two of them have nothing behind and just one of them has one million dollars in cash. First you have to pick a curtain, curtain #1, curtain #2, or curtain #3. Once you’ve made a selection the host will open one of the curtains that had nothing behind it and then offer you the chance to stay with the original choice or change curtains. (Note: that the host only opens a curtain that did not had the prize behind it)
a. Using Excel (or the software of your preference) do a Monte Carlo simulation for all the possible scenarios. Generate 100 replicas in the first sheet, 10,000 in the second, and 100,000 in the third. What’s the probability of winning if you chose to stay? Hint: use Excel functions and(), randbetween(), and if(). (Tip: Use one column to select the door, next column for the winning door and another column to say if you stayed or changed the selected door. Last door to say if you won)
b. Based on the results from part a, state which option is better: stay with your curtain or change. Justify the results from part a. Is this result intuitive, why or why not?
Explanation / Answer
Ans(a);
there is no option to upload that much huge amount of data so you can try making excel sheet yourself.
Ans(b):
Based on the results from part a, changing your choice is better option.
say you start with 10 curtains.
as there is just 1 correct item so probability of winning is 1/10 in the beginning.
Now 8 blank curtains are removed and only two curtains are left.
that include your choice.
Notice that 2nd left out curtain is actually clubbed with 8 blank curtains.
so practically you are getting option:
case1: stick with original choice whose probability is 1/10
case2: change the choice. that practically makes 9 curtains available for you to choose. which seems like probability of 9/10
obviously 9/10 is more than 1/10
so theoritically we see that changing the choice is better option.
Yes it is intuitive as I explained above.
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