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2
Posted on 7/23/18 at 2:49 pm to memphis tiger
quote:I have said that repeatedly.
While that is true, the ball can only be gold or silver, it does not mean there is a 50%chance the ball you choose will be silver.
While the outcome will only be gold or silver, the odds of the gold outcome are 2/3.
Posted on 7/23/18 at 2:52 pm to LSUBoo
quote:
Just happens that there are two gold balls potentially in play and only one silver.
each of them representing a unique statistical outcome.
That's why the answer is 2/3.
Posted on 7/23/18 at 2:56 pm to CptRusty
Once you picked the first ball and you learn it is gold, you know it is 2 times more likely that you picked the gold ball from a box with 2 gold options than from the box with 1 gold option. However, at that point, when you take the second ball out of the box, only 2 options remain. It is either the other gold ball or a silver ball.
Posted on 7/23/18 at 2:56 pm to 50_Tiger
quote:
I am trying to think of a way using combinations:
Eliminating the obvious now [S,S] and adding the fact you have successfully chosen a G ball, You are left 3 choose 1 combinations (3 comb) in two boxes: [G1,G2], [G3,S].
The combinations are:
G1,G2
G2,G1
G3,S
2 out of the 3 combinations (67%) grant you a successful outcome.
That's not why the answer is 67%. You can't eliminate the S,S box and not also eliminate either the G1,G2 or the G2,G1 combination after picking the first gold ball. One of those combinations is already eliminated.
The reason the answer is 67% is due, entirely, to the fact that IF your first pick was a gold ball then its more likely you have already selected the box with the 2 gold balls.
Posted on 7/23/18 at 2:57 pm to UpToPar
Thank you.
Posted on 7/23/18 at 2:58 pm to PearlJam
quote:
Uhhh... It is either silver or gold. They aren't all in the same box and a gold ball has been eliminated. It's either the gold ball that was in the box with a silver ball or it is one of the 2 gold balls that were once together.
Your explanation here says there are 3 possible outcomes, yet you argue otherwise.
Knowing we chose a gold ball leaves us with 2 possible BOXES, those boxes have 4 balls in them. We've seen one of the balls. There are 3 balls we haven't seen, ergo, 3 possible outcomes.
Posted on 7/23/18 at 2:58 pm to CptRusty
Let's do it like this. Anyone who doubts the 67% answer, answer these questions for me:
1. Before removing any balls, what is the likelihood you choose a gold ball if you're holding the GG box?
2. Same question as above, but the GS box?
3. Same as above, except now the SS box?
4. What is the likelihood you choose one of these 3 boxes at random?
Once someone answers all 4 correctly I'll show you why it's 67%
1. Before removing any balls, what is the likelihood you choose a gold ball if you're holding the GG box?
2. Same question as above, but the GS box?
3. Same as above, except now the SS box?
4. What is the likelihood you choose one of these 3 boxes at random?
Once someone answers all 4 correctly I'll show you why it's 67%
Posted on 7/23/18 at 2:59 pm to slackster
quote:
The reality of the situation is that your gold ball was one of 3 possible choices
No, No, No, No, No
Youre pulling a magicians trick by forcing a specific ball on me, but telling me I had three options to start with. I never had 3 options. By forcing the gold ball into my hand, you only allowed 2 options. It either came from the AG box or the M box. There never was the 3rd option of the AS box.
The probabilities are now strictly confined to whether I chose the AG box or the M box. It doesn't even matter what the next color I pull out is. I'm now limited to the only boxes that you allowed from the start, 2 (two). Its essentially flipping a coin at that point. It either turns up as box A or box B
Posted on 7/23/18 at 2:59 pm to slackster
quote:no. We are stuck with the original box and one ball (a gold one) has been removed. 1 ball of unknown color remains in the 1 box.
Knowing we chose a gold ball leaves us with 2 possible BOXES, those boxes have 4 balls in them
Posted on 7/23/18 at 2:59 pm to LSUBoo
quote:
Well, the next ball is either gold or silver... that's two possible color outcomes.
Just happens that there are two gold balls potentially in play and only one silver.
Yes. All of this is true.
There are two possible colors remaining.
There are 3 possible balls remaining.
Posted on 7/23/18 at 3:00 pm to PearlJam
quote:
no. We are stuck with the original box and one ball (a gold one) has been removed. 1 ball of unknown color remains in the 1 box.
By that logic there is only one outcome remaining - whatever ball is in the box is the only outcome it can be.
Posted on 7/23/18 at 3:01 pm to UpToPar
quote:
The reason the answer is 67% is due, entirely, to the fact that IF your first pick was a gold ball then its more likely you have already selected the box with the 2 gold balls.
Explain why, and show your work.
Posted on 7/23/18 at 3:01 pm to RobbBobb
quote:
No, No, No, No, No
Youre pulling a magicians trick by forcing a specific ball on me, but telling me I had three options to start with. I never had 3 options. By forcing the gold ball into my hand, you only allowed 2 options. It either came from the AG box or the M box. There never was the 3rd option of the AS box.
The probabilities are now strictly confined to whether I chose the AG box or the M box. It doesn't even matter what the next color I pull out is. I'm now limited to the only boxes that you allowed from the start, 2 (two). Its essentially flipping a coin at that point. It either turns up as box A or box B
This was run with a computer program that was run over a million times with the OP's scenario. It's been posted multiple times. The answer is 67%.
Posted on 7/23/18 at 3:02 pm to PearlJam
quote:
If you had a box with 3 gold balls, and another box with 1 gold ball and two silvers, what are the odds of pulling a second gold ball from the same box if your first pull resulted in gold. Once you can answer that, you will understand why it is important to consider each ball individually.
If you understand why the answer is 2/3 then solve that for me. Show your work.
Posted on 7/23/18 at 3:02 pm to RobbBobb
quote:
Youre pulling a magicians trick by forcing a specific ball on me, but telling me I had three options to start with. I never had 3 options. By forcing the gold ball into my hand, you only allowed 2 options. It either came from the AG box or the M box. There never was the 3rd option of the AS box.
By forcing the gold ball into your hand I left you with two possible boxes. If you can't understand that your chances of having the all gold box are twice as good as having the half and half box, there is no point in discussing this any further.
Posted on 7/23/18 at 3:02 pm to slackster
quote:well, we don't know which box we have, so it could be a gold ball left or it could be a silver. But we know when we pulled the first gold ball out, it was twice as likely to come from the box with 2 gold balls than from the box with only 1 gold ball.
By that logic there is only one outcome remaining - whatever ball is in the box is the only outcome it can be
Posted on 7/23/18 at 3:03 pm to PearlJam
Hey y'all... what if there were 4 boxes with:
GGG, GGS, GSS, SSS???
GGG, GGS, GSS, SSS???
Posted on 7/23/18 at 3:05 pm to ell_13
quote:
Hey y'all... what if there were 4 boxes with:
GGG, GGS, GSS, SSS???
Assuming we pulled a gold ball, the chance of the next ball being gold is 80%.
This post was edited on 7/23/18 at 3:06 pm
Posted on 7/23/18 at 3:07 pm to CptRusty
quote:
Explain why, and show your work.
If you reach into one of the three boxes and pull out a ball and it is gold, it had to come from 1 of the 2 boxes with a gold ball in it. Between those two boxes, one has 2 gold balls and the other has a single gold ball. Therefore, you are twice as likely to have selected a ball from the box with 2 gold balls. So, there is a 66.67% chance you selected the box with 2 gold balls and a 33.33% chance you selected the box with a single gold ball.
Once the first gold ball has been selected, you're next ball pulled with either be one of two possible outcomes: silver (33.33% chance) or gold (66.67% chance)
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