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re: Solve this OT
Posted on 7/23/18 at 1:45 pm to PearlJam
Posted on 7/23/18 at 1:45 pm to PearlJam
quote:
There are only 2 possible outcomes. 1 gold and 1 silver. The answer is still 67 percent though.
Wrong.
G1B1 is a single distinct outcome
G2B1 is a single distinct outcome
S1B2 is a single distinct outcome
1
Posted on 7/23/18 at 1:47 pm to CptRusty
He said after you pick the first 1. Once you have picked the first 1, there are only two outcomes, because there is only 1 ball left in the box. It will be either silver (33% of the time) or gold (67% of the time).
This post was edited on 7/23/18 at 1:49 pm
Posted on 7/23/18 at 1:48 pm to OweO
quote:
Once you pull out a gold ball, that eliminates the box with two gray balls. So that means, you have either pulled from the box with two gold balls or the box with one gold ball and one gray ball. At that point it is a 50/50 shot. Before someone pulls out a ball, the chance of pulling a gold ball is 1/3.
Here is another way to put it.
Call the all gold box Box #1. The half and half is Box #2. The all silver is Box #3.
You close your eyes and pick a box. You reach in and pull out a gold ball. Now I ask whether you think you've chosen Box #1 or Box #2? Which box do you think you chose?
Posted on 7/23/18 at 1:50 pm to PearlJam
We are talking semantics.
There are 3 possible scenarios depending on which gold ball you pulled first.
Two of those scenarios end in your second pull being a gold ball, although those gold balls are distinct from one another, they are both gold.
The third is pulling the silver ball.
There are 3 possible scenarios depending on which gold ball you pulled first.
Two of those scenarios end in your second pull being a gold ball, although those gold balls are distinct from one another, they are both gold.
The third is pulling the silver ball.
Posted on 7/23/18 at 1:51 pm to CptRusty
quote:Once you have pulled the gold ball, there are only 2 scenarios. However, math tells you one scenarios is more likely than the other.
There are 3 possible scenarios depending on which gold ball you pulled first.
Posted on 7/23/18 at 1:51 pm to PearlJam
quote:
Wrong. There are only 2 possible outcomes. 1 gold and 1 silver. The answer is still 67 percent though.
There are TWO remaining gold balls and one remaining silver ball, for a grand total of THREE possible outcomes.
I don't care that two of the balls are the same color. There are two ways of getting a gold ball.
Posted on 7/23/18 at 1:52 pm to LordSaintly
quote:
There are TWO remaining gold balls and one remaining silver ball, for a grand total of THREE possible outcomes.
I don't care that two of the balls are the same color. There are two ways of getting a gold ball.
Posted on 7/23/18 at 1:53 pm to PearlJam
quote:
He said after you pick the first 1. Once you have picked the first 1, there are only two outcomes, because there is only 1 ball left in the box. It will be either silver (33% of the time) or gold (67%) of the time.
Yeah, but thinking of it as either gold or silver muddles the conversation. Thinking of the balls as distinct items with a name helps people understand the math.
For example, change silver and gold to women and men. You've got a box with two men, John and James. You've got a box with two women, Lisa and Laura. You've got a mixed box with Jack and Jill.
You reach in and pick out a person, and it's a man. What are the chances the next person is a man?
Well, you either picked John, James, or Jack with the first pick. That leaves either John, James, or Jill as the remaining options, hence the 67%. Sure, it's either a man or a woman left, but the names matter.
Posted on 7/23/18 at 1:53 pm to PearlJam
quote:
Once you have picked the first 1, there are only two outcomes
Once you have picked 1 of 4 there are still 3 of 4 balls left.
Posted on 7/23/18 at 1:53 pm to LordSaintly
quote:nope. Your box is already chosen. Either you picked the one with 2 golds or you picked the one with a gold and silver. There aren't 3 possible outcomes at that point.
There are TWO remaining gold balls and one remaining silver ball, for a grand total of THREE possible outcomes.
Posted on 7/23/18 at 1:53 pm to PearlJam
Here's the setup:
You pick randomly from the 3 boxes as described meaning there's a 33.3% chance you pick a gold from box 1 and a 16.7% chance you pick gold from box 2 (adding up to 50% since half the 6 balls are gold). This means that from the initial choice, you are 16.7% more likely to chose the box with the two golds. So while there are two boxes left and the result would be either gold or silver (50/50), it's actually more likely to be gold by another 16.7%... So 66.7%.
That's the proof from a mathematical standpoint starting with the initial percentages. Other proofs have been given using simulations as well as the possible scenarios.
You pick randomly from the 3 boxes as described meaning there's a 33.3% chance you pick a gold from box 1 and a 16.7% chance you pick gold from box 2 (adding up to 50% since half the 6 balls are gold). This means that from the initial choice, you are 16.7% more likely to chose the box with the two golds. So while there are two boxes left and the result would be either gold or silver (50/50), it's actually more likely to be gold by another 16.7%... So 66.7%.
That's the proof from a mathematical standpoint starting with the initial percentages. Other proofs have been given using simulations as well as the possible scenarios.
Posted on 7/23/18 at 1:55 pm to PearlJam
quote:
PearlJam
Although you are giving the correct answer (67%), you don't actually understand how to get the answer.
Read through the analogy posted which substitutes men/women for gold/silver. It may help.
Posted on 7/23/18 at 1:56 pm to CptRusty
I do. You are missing the point. Once you have picked a gold ball, there aren't 3 distinct outcomes. There are only 2.
This post was edited on 7/23/18 at 1:57 pm
Posted on 7/23/18 at 1:57 pm to slackster
quote:
Sure, it's either a man or a woman left, but the names matter.
Exactly. The balls are distinct.
This post was edited on 7/23/18 at 1:57 pm
Posted on 7/23/18 at 1:57 pm to PearlJam
quote:
nope. Your box is already chosen. Either you picked the one with 2 golds or you picked the one with a gold and silver. There aren't 3 possible outcomes at that point.
I understand what you're saying, but people have a hard time visualizing it that way.
Posted on 7/23/18 at 1:58 pm to slackster
That's fine, but the comment I responded to was wrong. That's all.
Posted on 7/23/18 at 1:58 pm to PearlJam
quote:
nce you have picked a gold ball, there aren't 3 distinct outcomes. There are only 2.
then why aren't the odds 50/50?Posted on 7/23/18 at 1:59 pm to CptRusty
quote:because there is a greater chance you pulled a gold ball from the box with 2 gold balls than if you pulled the gold ball from the box with one gold and one silver.
then why aren't the odds 50/50?
Posted on 7/23/18 at 2:00 pm to PearlJam
quote:
. Once you have picked a gold ball, there aren't 3 distinct outcomes. There are only 2.
While you may have 2 types of outcome remaining (You pick Gold or you pick Silver) There is still a 2xs greater chance that you will pick the gold outcome. That is what the question is asking.
G1 B1
G2 B1
S1 B2
Those are your options for Pick #2.
Posted on 7/23/18 at 2:01 pm to PearlJam
quote:
I do. You are missing the point. Once you have picked a gold ball, there aren't 3 distinct outcomes. There are only 2.
Once we pick a man, we know the next person is either John, James, or Jill.
If we KNOW we picked John first, then there is only one outcome left. If we know we picked James first, there is only one outcome left. If we know we picked Jack first, there is only one outcome left.
However, all we know is that we picked a man. We still don't know which box we have. We don't know if we're going to pull out John, James, or Jill next.
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