Deleted
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Post by Deleted on Sept 11, 2012 23:18:13 GMT -5
I still say it doesnt make a hill of beans whether you swap or not.
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Post by 101mitch on Sept 12, 2012 15:44:19 GMT -5
OMG. My CPU froze when I had a like paragraph long rant on this! lol
Look at it this way; Starts with 2/3 probability of getting a goat, 1/3 of getting a car.
You choose. The host then opens a goat. Making the denominator two because only two doors are left. There is only one goat left and two doors making the probability 1/2. There is only one car left, and two doors making the probability 1/2!!
IT MAKES NO DIFFERENCE!
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cbagin
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Post by cbagin on Sept 12, 2012 16:12:52 GMT -5
OMG. My CPU froze when I had a like paragraph long rant on this! lol Look at it this way; Starts with 2/3 probability of getting a goat, 1/3 of getting a car. You choose. The host then opens a goat. Making the denominator two because only two doors are left. There is only one goat left and two doors making the probability 1/2. There is only one car left, and two doors making the probability 1/2!! IT MAKES NO DIFFERENCE! Not true. You started with a 2/3 chance of getting a goat and 1/3 chance of getting the car. As he explains, once they open the door showing the goat, you now have a 66% chance of getting the car if you swap. In simplest terms, You START OUT with a 33% chance of car So you MOST LIKELY drew a goat. That means that once he shows you the other goat, you now MOST LIKELY will swap to a car. He explains it well in the film, and I see where you're coming from, however, the guy is right. The thing to do is swap if you want to play the percentages.
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Post by 101mitch on Sept 12, 2012 16:20:08 GMT -5
OMG. My CPU froze when I had a like paragraph long rant on this! lol Look at it this way; Starts with 2/3 probability of getting a goat, 1/3 of getting a car. You choose. The host then opens a goat. Making the denominator two because only two doors are left. There is only one goat left and two doors making the probability 1/2. There is only one car left, and two doors making the probability 1/2!! IT MAKES NO DIFFERENCE! Not true. You started with a 2/3 chance of getting a goat and 1/3 chance of getting the car. As he explains, once they open the door showing the goat, you now have a 66% chance of getting the car if you swap. In simplest terms, You START OUT with a 33% chance of car So you MOST LIKELY drew a goat. That means that once he shows you the other goat, you now MOST LIKELY will swap to a car. He explains it well in the film, and I see where you're coming from, however, the guy is right. The thing to do is swap if you want to play the percentages. No. Just no. Look. You start out with a 66% chance of getting a goat, 33% chance of getting a car!!!! Right? We agree correct? As soon as he opens the goat door the percentage HAS to drop because he just opened a goat, meaning it went from two goats to one goat! So instead of 2/3 it goes to 1/2. Right? Because ONE goat is left, and TWO doors. Tell if that seems wrong to you. Now with the car. The car starts as 1/3, but when the door gets opened and it isn't a car the probability HAS to go up. Because there is only one car and two doors the probability is 1/2. Meaning they are both 1/2 and both 50%!
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Post by Jindred on Sept 12, 2012 21:23:59 GMT -5
Not true. You started with a 2/3 chance of getting a goat and 1/3 chance of getting the car. As he explains, once they open the door showing the goat, you now have a 66% chance of getting the car if you swap. In simplest terms, You START OUT with a 33% chance of car So you MOST LIKELY drew a goat. That means that once he shows you the other goat, you now MOST LIKELY will swap to a car. He explains it well in the film, and I see where you're coming from, however, the guy is right. The thing to do is swap if you want to play the percentages. No. Just no. Look. You start out with a 66% chance of getting a goat, 33% chance of getting a car!!!! Right? We agree correct? As soon as he opens the goat door the percentage HAS to drop because he just opened a goat, meaning it went from two goats to one goat! So instead of 2/3 it goes to 1/2. Right? Because ONE goat is left, and TWO doors. Tell if that seems wrong to you. Now with the car. The car starts as 1/3, but when the door gets opened and it isn't a car the probability HAS to go up. Because there is only one car and two doors the probability is 1/2. Meaning they are both 1/2 and both 50%! It does make a difference.. Its 50% between the last two yes! that is true you've got that correct. However, because it was 66% likely that you picked the goat in the first place it is better to switch! You have more likely already picked the goat than the car so its more likely that the other choice is now the car!
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cbagin
College Starter
Crunch Time
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Post by cbagin on Sept 12, 2012 21:26:58 GMT -5
No. Just no. Look. You start out with a 66% chance of getting a goat, 33% chance of getting a car!!!! Right? We agree correct? As soon as he opens the goat door the percentage HAS to drop because he just opened a goat, meaning it went from two goats to one goat! So instead of 2/3 it goes to 1/2. Right? Because ONE goat is left, and TWO doors. Tell if that seems wrong to you. Now with the car. The car starts as 1/3, but when the door gets opened and it isn't a car the probability HAS to go up. Because there is only one car and two doors the probability is 1/2. Meaning they are both 1/2 and both 50%! It does make a difference.. Its 50% between the last two yes! that is true you've got that correct. However, because it was 66% likely that you picked the goat in the first place it is better to switch! You have more likely already picked the goat than the car so its more likely that the other choice is now the car! Jindred is right. The bold is what i was really trying to say simplified.
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Post by 101mitch on Sept 12, 2012 22:10:58 GMT -5
GUYS!!! Who gives about the beginning of the problem?? All that matters is that as soon as that door is opened EVERYTHING changes. When he opens the goat you now KNOW FOR A FACT that there is only ONE GOAT LEFT.
When the door is opened it is unimportant. Leaving you with two doors. If you have two doors and one is a goat what is the probability? 1/2. Tell me if I am wrong about that.
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Deleted
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Post by Deleted on Sept 12, 2012 22:13:08 GMT -5
It doesnt matter if you switch or not. We should have a poll.
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Post by Jindred on Sept 12, 2012 22:18:42 GMT -5
GUYS!!! Who gives about the beginning of the problem?? All that matters is that as soon as that door is opened EVERYTHING changes. When he opens the goat you now KNOW FOR A FACT that there is only ONE GOAT LEFT. When the door is opened it is unimportant. Leaving you with two doors. If you have two doors and one is a goat what is the probability? 1/2. Tell me if I am wrong about that. Yes you are right that between the two doors left it is a 50/50 chance. However that's not the only thing in play! because there was a third door things are different. Getting rid of the third door does not change the fact that you have already more likely picked the goat... So if you stay with that its still 66% likely that you have picked the goat! So its better to change! It took me three days to get this I was absolutely baffled by it until it clicked.. but its true! Its on myth busters and the math works out.
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Post by lostabroad2 on Sept 13, 2012 0:00:15 GMT -5
Once the goat is revealed there are 2 doors left. However it is not a 50-50 choice! They are not equally likely to have the car behind them. The door you originally chose is a 1in 3 chance. The other door is now a 2 in 3 chance. Thus, sticking will be correct only 33.333% of the time and switching will be correct 66.667% of the time.
Most of you will have difficulty in hiding a car and 2 goats behind 3 doors in your own homes so try this game instead. Shuffle a pack of playing cards and then spread them out face down on a table. You're trying to pick the Queen of Hearts. You pick a card and move it to your left. The remaining 51 cards are moved to your right. The chance of the Queen being on your left is 1 in 52. The chance of it being to your right is 51 in 52. If you have picked the Queen, (1 in 52), there will be 51 wrong cards to your right. If you picked a wrong card, (51 in 52, there will be 50 wrong cards and the Queen of Hearts to your right. 50 losing cards are now removed from the pile of cards to your right and moved to the middle of the table. There is 1 card face down to your left. There is 1 card face down to your right. There are 50 losing cards face down in the middle of the table. The chance of the Queen being in the pile of losing cards is 0 in 52. There are now 2 possibilities left. Your original choice and the 1 remaining after the losing options were removed. This is in effect the same scenario as in the Monty Hall Problem. Either they are both equally likely, (I.E a 1 in 2 probability/50% chance), or your original choice is the same probability now as it was when you originally picked it, (I.E a 1 in 52 probability).
The chance of the Queen being on your left is still 1 in 52. The chance of it being to your right is still 51 in 52. The card to your left is not altered or changed when the 50 cards are revealed. If you originally picked the Six of Clubs then it will remain as the Six of Clubs. If it was right when you picked it will still be right. If it was wrong when you picked it will still be wrong.
The long-winded route: If you originally picked the Ace of Clubs, (a 1 in 52 chance). 50 wrong cards are removed from the 51 cards to your right and the remaining card will be the Queen of Hearts. The probability of this event is 1 in 52. If you originally picked the Two of Clubs, (a 1 in 52 chance). 50 wrong cards are removed from the 51 cards to your right and the remaining card will be the Queen of Hearts. The probability of this event is 1 in 52. If you originally picked the Three of Clubs, (a 1 in 52 chance). 50 wrong cards are removed from the 51 cards to your right and the remaining card will be the Queen of Hearts. The probability of this event is 1 in 52. If you originally picked the Four of Clubs, (a 1 in 52 chance). 50 wrong cards are removed from the 51 cards to your right and the remaining card will be the Queen of Hearts. The probability of this event is 1 in 52. I'm hoping you don't need me to post all 52 possible outcomes. Suffice to say that if you originally picked the right card then the remaining card to your right would be 'a wrong card'. It doesn't much matter here which wrong card it is. The probability of this event is 1 in 52.
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