Would you switch?
- Thread starter traderich
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If you think it is BS, all I can say is that you are mathematically challenged (to put it politely)
Quote from candletrader:
If you think it is BS, all I can say is that you are mathematically challenged (to put it politely)
Could be.. but I got As in Calculus and have degree in chemistry...
Quote from candletrader:
If you think it is BS, all I can say is that you are mathematically challenged (to put it politely)
Could be.. but I got As in Calculus and was a Summa Cum Laude* graduate in chemistry...
This, however, is not a math problem as much as a logic problem.
*meaning, I got As in pretty much EVERYTHING!... I admit it... earned a "B" in a physics course once, and it DID piss me off...
No switch
1/3 x 1/2 = 1/6 you have to be right in both of your choices
Switch
2/3 x 1/2 = 2/6 yor are saying screw the first choce, let me switch, this replaces the probability of the first step to the opposite of the 1/3 which is 2/3, you still have to be correct on the second choice which brings the total to 2/6
You must know that the sum of all probabilities for a given choice must equal 1
So
P for the first choice is 0.33 the opposite of this choice is 1- p or 0.66 or 2/3 this is why deciding to switch, replaces 1/3 with 2/3
The above assumes that the host knew where the winer is. This is why switching replaces 1/3 with 2/3, him opening the door is not a guess. He is helping you by reducing the options.
If the the host didn't know where the winer is the equation changes (his choice is a guess and it must be included into the total probability calculation)
1/3 for your first choice multiplied by 1/2 for the host choice multiplied by 1/2 for your second choice regardless if you choose to switch or not. So it doesn't matter if you decide to switch or not it is 50:50 at that point.
1/3 x 1/2 = 1/6 you have to be right in both of your choices
Switch
2/3 x 1/2 = 2/6 yor are saying screw the first choce, let me switch, this replaces the probability of the first step to the opposite of the 1/3 which is 2/3, you still have to be correct on the second choice which brings the total to 2/6
You must know that the sum of all probabilities for a given choice must equal 1
So
P for the first choice is 0.33 the opposite of this choice is 1- p or 0.66 or 2/3 this is why deciding to switch, replaces 1/3 with 2/3
The above assumes that the host knew where the winer is. This is why switching replaces 1/3 with 2/3, him opening the door is not a guess. He is helping you by reducing the options.
If the the host didn't know where the winer is the equation changes (his choice is a guess and it must be included into the total probability calculation)
1/3 for your first choice multiplied by 1/2 for the host choice multiplied by 1/2 for your second choice regardless if you choose to switch or not. So it doesn't matter if you decide to switch or not it is 50:50 at that point.
The above (answer, and reason) are correct... as anyone who has read Nassim Talebâs âFooled by Randomness: The Hidden Role of Chance in Life and in the Marketsâ (which in includes me, and presumably also the OP?) will know.
I found it easier to understand the answer more intuitively by first forgetting the original question for a moment, and just focusing on the following one; once I understood it, I understood better the correct answer to the original problem.
Restated problem:
- You have 100 doors to choose from. You pick one door.
- One is a winner, the other 99 are losers.
You choose a door and 98 of the other 99 doors are revealed to show they are losers.
Question: Now that 98 of the other 99 doors have been revealed to show they are losers, would you now switch your original choice to the other remaining unopened door?
Right... Your self proclaimed genius level aside, you obviously lack the common sense to figure out why you switch everytime. You could draw out a tree of possibilities but maybe you do not know how to do that.
It's real simple, when you pick with 3 doors, you have 1/3rd chance of being right. When one wrong door is eliminated you can only improve your odds by switching your pick.
Come on, it's simple. When you picked the first time you had a 33% chance. At this point, if you switch, it means you're giving up the door which you have now confirmed is not one of the two doors which are losers. That means there is only one losing door left, which now gives you a 66.6% chance of being right if you keep the same door.
Your mind may have just been blown away. Whoooosh.
Think about. Go back to the original.
Your mind may have just been blown away. Whoooosh.
Think about. Go back to the original.