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Fri Dec 21, 2012, 10:27 AM

Having a probability mental block

Problem 1:

I have a bag of 136 unique items.

I reach into the bag, pull out one item.

I return the item to the bag.

I do this 45 times.

After the 45 draws from the bag, how many different unique items have I drawn?

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Problem 2:

I have a bag of 136 unique items.

I reach into the bag and pull out three items.

I return the items to the bag.

I do this 15 times.

After the 15 draws, how many different unique items have I drawn?

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I'm coming up with about 38 for Problem 1, and about 43 for Problem 2, rounding to the nearest whole number.

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Reply Having a probability mental block (Original post)
jberryhill Dec 2012 OP
Jackpine Radical Dec 2012 #1
jberryhill Dec 2012 #2
tama Dec 2012 #3
jberryhill Dec 2012 #4
tama Dec 2012 #6
jberryhill Dec 2012 #7
Jackpine Radical Dec 2012 #8
jberryhill Dec 2012 #9
Festivito Dec 2012 #5

Response to jberryhill (Original post)

Fri Dec 21, 2012, 10:37 AM

1. 1) A minimum of 1, a max of 45

2) A min of 3, a max of 45.

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Response to Jackpine Radical (Reply #1)

Fri Dec 21, 2012, 10:47 AM

2. Yeah, yeah... solve for 0, 1, infinity, and everything else is a special case....

Oy.

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Response to jberryhill (Original post)

Fri Dec 21, 2012, 10:50 AM

3. 45 and 15

 

it really is that simple, if you don't confuse your thinking by various interpretations of Law of Identity.

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Response to tama (Reply #3)

Fri Dec 21, 2012, 10:56 AM

4. Perhaps I didn't state the problem clearly enough


After each draw, the items are returned to the bag.



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Response to jberryhill (Reply #4)

Fri Dec 21, 2012, 11:54 AM

6. That was understood

 

http://en.wikipedia.org/wiki/Law_of_identity A=A is necessary presumption for bivalent logic and http://en.wikipedia.org/wiki/Law_of_excluded_middle

But I see no logical necessity to believe in Law of Identity and state that the returned item would be identical with the drawn item. After each draw-return process the bag still consists of unique items regardless of the number of draws.

Note that spatiotemporally etc. in physical terms the left and right parts of Law of Identity A=A are not identical.

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Response to tama (Reply #6)

Fri Dec 21, 2012, 12:49 PM

7. I'm dealing with an issue relating to jury pools

And I assure you that when the jurors are sent back to the pool room, they are each the same person the next time they are called. Okay?

Without getting into a lot of specifics, the case involves an allegation of bias in juror selection.

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Response to jberryhill (Reply #7)

Fri Dec 21, 2012, 01:35 PM

8. So you're asking for the probability distributions.

I think it's a cumulative combination problem & I'd have to look up the solution, unfortunately. Too many years since I studied or taught that stuff.

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Response to Jackpine Radical (Reply #8)

Fri Dec 21, 2012, 01:38 PM

9. Not the distributions


Just a back of the envelope expectation value. I don't even care what the variance is.

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Response to jberryhill (Original post)

Fri Dec 21, 2012, 11:39 AM

5. 39-40 certain for 1 and 80+% chance of 45 for 2.

But, it's been a loooooong time.

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