# Indistinguishable Objects in Probability

**URL:** <https://boards.straightdope.com/t/indistinguishable-objects-in-probability/626548>\
**Category:** Factual Questions\
**Created:** [June 28, 2012, 5:45am UTC](https://boards.straightdope.com/t/indistinguishable-objects-in-probability/626548 "2012-06-28T05:45:16Z")\
**Posts on this page:** 2\
**Page:** 2

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**Author:** ![Indistinguishable](https://avatars.discourse-cdn.com/v4/letter/i/90ced4/32.png) [@Indistinguishable](https://boards.straightdope.com/u/Indistinguishable)\
**Post date:** [July 1, 2012, 8:20pm UTC](https://boards.straightdope.com/t/indistinguishable-objects-in-probability/626548/21 "2012-07-01T20:20:10Z")

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Do they? Suppose, for simplicity, we used two 2-sided dice (i.e., coins).

Then: 1/4 of the time we get a head and a tail (we get both behind the divider 1/2 the time, and we pull both in front of the divider 1/2 the time), 3/8 of the time we get two heads, and 3/8 of the time we get two tails. I don’t know anything about quantum mechanics, but I thought the “indistinguishable” stats we were going for would make these all equal.

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**Author:** ![Andy\_L](https://avatars.discourse-cdn.com/v4/letter/a/c67d28/32.png) [@Andy\_L](https://boards.straightdope.com/u/Andy_L)\
**Post date:** [July 1, 2012, 8:31pm UTC](https://boards.straightdope.com/t/indistinguishable-objects-in-probability/626548/22 "2012-07-01T20:31:04Z")

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> [@Indistinguishable](#):
>
> Do they? Suppose, for simplicity, we used two 2-sided dice (i.e., coins).
> 
> Then: 1/4 of the time we get a head and a tail (we get both behind the divider 1/2 the time, and we pull both in front of the divider 1/2 the time), 3/8 of the time we get two heads, and 3/8 of the time we get two tails. I don’t know anything about quantum mechanics, but I thought the “indistinguishable” stats we were going for would make these all equal.

You’re right. For distinguisable coins, you get probabilities for HH, TT and non-matched coins of 1/4, 1/4, and 1/2. For indistinguishable coins, you’d want the probabilities to be 1/3 each. For the method I came up with, the probabilities are 6/16, 6/16, and 4/16, which are closer to the indistinguishable case, but not quite there. [Emily Litella]Never mind[/Emily Litella]

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