Lose your marbles

[DWC28]

You have three bags, each containing two marbles. Bag A contains two white marbles, Bag B contains two black marbles, and Bag C contains one white marble and one black marble.

You pick a random bag and take out one marble.

It is a white marble.

What is the probability that the remaining marble from the same bag is also white?

 

[theKman]

50/50.

 

[440Magnum]

0.5

-By picking a white marble, you've eliminated the bag with 2 black marbles. So you know you're dealing with bag A or bag C.

-If its bag A, you already picked a white marble so the other will be white.

-If its bag C, you already picked the white marble so the other will be black.

So it only depends on whether you picked Bag A or Bag C. 50/50 chance.

 

[mrsilv04]

I adopted a dog, his name was Marbles.

I had to change his name, as I didn't want to risk ever losing my Marbles.






Sorry... but this is true.

 

[KGMtech]

I can't answer because this is once again a struggle between White and Black ~ we have to get past seeing colours and just choose marbles. Amen )

 

[tomcat27]

all marbles matter

 

[DWC28]

Spoiler Alert

Run the problem 18,000 times.
You should probably get the following results
6,000 both black
6,000 both white
3,000 first white, second black
3,000 first black, second white

Since you are only interested in the first marble being white you can throw out all the results where the first was black.
That leaves 9,000 possibles and 6,000 of those are white, so the odds are


2/3.

 

[weasley]

0.5 - as stated above, and logically described by 440Magnum. You can completely remove bag B from the discussion, since it is irrelevant. So it comes down to two bags. After picking a white, one would have a white left and one would have a black left. It is 50:50.

 

[javacontour]

This seems very similar to the Monty Hall problem.

https://en.wikipedia.org/wiki/Monty_Hall_problem

 

[Alfred_B]

Originally Posted By: DWC28
Spoiler Alert

Run the problem 18,000 times.
You should probably get the following results
6,000 both black
6,000 both white
3,000 first white, second black
3,000 first black, second white

Since you are only interested in the first marble being white you can throw out all the results where the first was black.
That leaves 9,000 possibles and 6,000 of those are white, so the odds are


2/3.


2/3 would be my answer, too.

 

[kschachn]

Originally Posted By: javacontour
This seems very similar to the Monty Hall problem.
https://en.wikipedia.org/wiki/Monty_Hall_problem


I don't think so. I remember studying the Monty Hall Problem for a couple of days in a Statistics & Probability class in college. In that problem, Monty knows what door has the car and he deliberately picks neither the "car" door nor your door. That skews the probability in your final choice. This is more like the "Monty Doesn't Know" version where he picks a random door.

 

[javacontour]

Remember, in this problem you know the first marble you picked was white. Therefore, I believe it is very similar.

This isn't a random issue. You already know something from the first choice, you got a white marble.

What if we said it was the Monty Hall problem in reverse, you picked a white marble, should you switch bags? The answer is no in this scenario. If you picked a white marble on your first draw, 2/3rds of the 1st white ball scenarios are you picked the bag with two white marbles, stay with your bag.

 

[BRZED]

The odds are 2/3.