Having a probability mental block

[jberryhill]

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.

[Jackpine Radical]

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

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

[jberryhill]

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

Oy.

[tama]

3. 45 and 15

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

[jberryhill]

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

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

[tama]

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.

[jberryhill]

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.

[Jackpine Radical]

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.

[jberryhill]

9. Not the distributions

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

[Festivito]

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

But, it's been a loooooong time.