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Started By
Message
re: Solve this OT
Posted on 7/23/18 at 10:57 am to TheMailman
Posted on 7/23/18 at 10:57 am to TheMailman
quote:
Let me try this one more time. I think we all agree that in this question from the OP that you have to pick the second ball from the same box from which you picked the first one.
You cant change boxes after the first pick.
There is a 1/3rds chance that the box you pick has two gold balls. Those odds never change !!! The odds would only change if I were allowed to pick a different box on the second pick.
If we had 100 boxes and 99 boxes had one silver ball and one gold ball and only 1 box had two gold balls.
I pick a box from the stage and hold it in my lap. I pull a ball out and its gold. What are the odds that the next ball I pick from that same box is gold?
1/100 …. The odds don't suddenly change after I pick that first ball out of the box.
The question is not asking what are the odds you picked the box with 2 gold balls.
The question is asking that once you definitively know that you dont have the all silver box, what are the odds that the remaining ball in your box is gold. There are 3 possible outcomes since you dont know which of the 2 remaining boxes you have. 2 of those possibilities are gold.
1
Posted on 7/23/18 at 10:58 am to TheMailman
quote:
There is a 1/3rds chance that the box you pick has two gold balls. Those odds never change !!!
After you pick the box and see it is a gold ball, you know the SS box is no longer in play for evaluating the remaining ball. So the odds do change.
Posted on 7/23/18 at 10:58 am to ell_13
quote:
You’ve thus chosen a gold coin from the first two boxes. There are three gold coins among them, and thus if you picked a gold coin on your first draw, the probability that you chose from box #1 is 2/3. The probability that you chose it from box #2 is 1/3.
If you chose from box #1, the probability that you will then draw a second gold coin is 1 (100%).
If you chose from box #2, the probability that you will then draw a second gold coin is 0 (0%) for there are no gold coins left.
Thus, the overall probability that if you got a gold coin on the first pick then you will get another one if drawing from the same box is (2/3 X 1) + (1/3 X 0), or 2/3 (probability 67%). The answer is thus 2/3 (probability 67%).
Posted on 7/23/18 at 10:59 am to TheMailman
You are hopeless. Absolutely hopeless.
Posted on 7/23/18 at 11:00 am to memphis tiger
quote:
The question is not asking what are the odds you picked the box with 2 gold balls.
In context, it’s the same answer.
Once you’ve selected the gold ball, there is a 2/3 chance you picked the double gold box and that is still a 2/3 chance your second pick will be gold.
Posted on 7/23/18 at 11:02 am to TheMailman
quote:
The odds don't suddenly change after I pick that first ball out of the box.
Of course they do. Your odds on the first choice were 1/100.
When you pull another ball you're looking at a different set of odds.
Posted on 7/23/18 at 11:02 am to ell_13
But I am not allowed to pick a box for my second draw. IT HAS TO BE FROM THE BOX I ORIGINALLY PICKED.
Posted on 7/23/18 at 11:03 am to 50_Tiger
40%
*eta* Didn't realize this was 9 pages long. Not reading through this shite.
*eta* Didn't realize this was 9 pages long. Not reading through this shite.
This post was edited on 7/23/18 at 11:05 am
Posted on 7/23/18 at 11:04 am to TheMailman
quote:
IT HAS TO BE FROM THE BOX I ORIGINALLY PICKED
WHAT ARE THE ODDS YOU PICKED THE BOX WITH TWO GOLD BALLS, KNOWING BEFOREHAND THAT ONE OF YOUR PICKS WILL DEFINITELY BE GOLD?????
Posted on 7/23/18 at 11:05 am to monkeybutt
I could post the Bayes' Theorem formula from wiki because it addresses the 1/3 that Mailman is thinking of but talk about blowing up this thread 
Posted on 7/23/18 at 11:05 am to TheMailman
quote:Yes, but since you know you picked a gold ball, the odds you picked the box with 2 gold balls is greater than the odds you picked the box with one gold ball.
IT HAS TO BE FROM THE BOX I ORIGINALLY PICKED.
Posted on 7/23/18 at 11:05 am to TheMailman
quote:
But I am not allowed to pick a box for my second draw. IT HAS TO BE FROM THE BOX I ORIGINALLY PICKED.
Is there something about not ever picking a silver ball first that you can't grasp?
Posted on 7/23/18 at 11:06 am to TheMailman
quote:
There is a 1/3rds chance that the box you pick has two gold balls. Those odds never change !!! The odds would only change if I were allowed to pick a different box on the second pick.
There’s a 1/3 chance you pick the box with 2 golds, sure.
There’s a 50% chance you pick a gold ball, sure.
But when you pick the gold ball, your chances increase because 1/3 of the boxes and 1/2 of the balls are discounted now.
There are no longer 3 boxes and 6 balls. There are 2 boxes and 3 balls. Once you pick gold, you know you picked one of 3 options:
Gold 1
Gold 2
Gold in the split box.
There is a 2/3 chance that if you selected a gold ball, it was from the double gold box; therefore, there is a 2/3 chance you will select a second gold ball.
This post was edited on 7/23/18 at 11:07 am
Posted on 7/23/18 at 11:07 am to TheMailman
quote:That's not the situation presented. This isn't asking "what's the probability of picking the box with 2 golds". This is after you have a gold in your hand. There is ZERO chance of having a silver in your hand so 33% was never a possibility.
IT HAS TO BE FROM THE BOX I ORIGINALLY PICKED.
Posted on 7/23/18 at 11:10 am to Havoc
quote:
After you pick the box and see it is a gold ball, you know the SS box is no longer in play for evaluating the remaining ball. So the odds do change.
BUT BUT BUT .. I do not have a choice of what box to pick the second ball from … I totally agree with you IF they allowed me to pick a box at random for that second pick.
Posted on 7/23/18 at 11:11 am to TheMailman
quote:
BUT BUT BUT .. I do not have a choice of what box to pick the second ball from … I totally agree with you IF they allowed me to pick a box at random for that second pick.
I just have no words.
Posted on 7/23/18 at 11:12 am to monkeybutt
quote:
Is there something about not ever picking a silver ball first that you can't grasp?
That option was never ruled out.
Posted on 7/23/18 at 11:13 am to TheMailman
quote:
That option was never ruled out.
it is explicitly ruled out.
quote:
You put your hand in and take a ball from that box at random. It's a gold ball.
This post was edited on 7/23/18 at 11:15 am
Posted on 7/23/18 at 11:13 am to TheMailman
quote:Annnnndddddd...
That option was never ruled out.
I'm done.
Posted on 7/23/18 at 11:13 am to TheMailman
quote:
But I am not allowed to pick a box for my second draw. IT HAS TO BE FROM THE BOX I ORIGINALLY PICKED
And you know with 100% certainty that that box had AT LEAST one gold ball.
You also know with 100% certainty that, of the 3 remaining balls 2 are gold.
Since you don’t know with 100% certainty which gold ball containing box you have, odds that the remaining ball being gold are 2/3.
Are you still arguing that the odds are 1/3???
This post was edited on 7/23/18 at 11:15 am
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