Subject:
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Re: math question (or pattern... whatever...)
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Newsgroups:
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lugnet.off-topic.geek
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Date:
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Mon, 3 Mar 2003 22:39:31 GMT
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Viewed:
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269 times
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In lugnet.off-topic.geek, David Koudys writes:
> k, here's something that came across my desk...
>
> you have a bag with 4 marbles in it.
>
> 2 of the marbles are red
> 1 marble is white
> 1 marble is blue
>
> you reach in and grab 2 random marbles
>
> you open up your hand a bit to only see the colour of one of those 2
> marbles, and it happens to be red
>
> what is the chance that the other marble in your hand is also red?
>
> I say it's 33 percent
> my friend says it's 20 percent
>
> I worked it out like this:
>
> 4 marbles:
>
> r r b w
>
> you grab 2, one is red so you immediately know that one of the red's doesn't
> have to be counted.
>
> so you're left with
>
> r b w
>
> that may be in your hand
>
> so one in 3 = 33 percent
>
>
> My friend calculated it this way
>
> r(1) r(2) b w
>
> the 'event' is that you have 2 balls in your hand, one of which is red
>
> so out of all the possible unique combinations (6)--
>
> r(1) r(2)
> r(1) b
> r(1) w
> r(2) b
> r(2) w
> b w
>
> the last one (b w) is eliminated 'cause you already know that there is a red
> in your hand, so the last one isn't part of 'the event'
>
> so the possibility of the second marble being red is 1 in 5, or 20 percent.
>
> but what my friend won't admit to, is that if you have
>
> r(1) r(2)
> r(1) b
> r(1) w
> r(2) b
> r(2) w
>
> (b w being still eliminated due to red already being in your hand) that a
> last possible combination:
>
> r(2) r(1)
>
> fits into the mix, so 2 out of 6, which still equals 33 percent
>
> Any stats people out there that could shed logic on this?
Your friend has assumed that there is a difference between the reds, and you
know which one you have seen in your hand. As there is no information in the
original problem to substantiate this assumption, you have to assume it's
not the case, so the valid combinations are in fact:
r,r
r,b
r,w
b,w
Your friend rightly discounted the b,w combination, which leaves 3, of which
yours must be one, therefore you are correct, the chances are 33%.
ROSCO
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Message has 1 Reply:
 | | Re: math question (or pattern... whatever...)
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| In lugnet.off-topic.geek, Ross Crawford writes: <snip> (...) I like driving home from work--gives me time to think about stuff... And after reading all the great replies, I'm going to propose the following solution: If you have a bag with 4 marbles, (...) (22 years ago, 3-Mar-03, to lugnet.off-topic.geek)
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Message is in Reply To:
| | math question (or pattern... whatever...)
|
| k, here's something that came across my desk... you have a bag with 4 marbles in it. 2 of the marbles are red 1 marble is white 1 marble is blue you reach in and grab 2 random marbles you open up your hand a bit to only see the colour of one of (...) (22 years ago, 3-Mar-03, to lugnet.off-topic.geek)
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