Math odds question

[MURP]

some peeps at work arguing over this odds question, so im coming to the  brain trust.

There are 10 names in a hat.   You pick out a name, read it, and put it back in the hat so there are still 10 names in the hat.  What are the odds of picking the same name out 3 times in a row?

[Susquehanna Birder]

1000 to 1.

[Sgt PSN]

What color is the hat?  

[Sgt PSN]

Sus, are you sure or just throwing a guess out there?  That's what I came up with too.   

Obviously, the odds on the first pull would be 10 to 1.

Multiply by 10 on the second pull and it's 100 to 1.

Multiply by 10 on the third pull and it's 1000 to 1. 

[PoopyfaceMcGee]

What they said.

[Sgt PSN]

I'd still like to know what color the hat is though. 

[MURP]

the hat color is a touch of Mauvelous splashed with Cerulean. 

thanks Sus. 

[Cerevant]

One important distinction: while the probability  of pulling the same name out of the hat 3 times in a row is 1/1000, the probability of pulling a given name on the 3rd try (or nth try) is still 1/10.  Past performance does not predict future results, and all that...

[phattymatty]

i got pocket aces 3 times in a row the other night playing poker.  someone tell me those odds.  i don't even know how to start.

[Rome]

i got pocket aces 3 times in a row the other night playing poker.  someone tell me those odds.  i don't even know how to start.

1,300:1

[Susquehanna Birder]

Sus, are you sure or just throwing a guess out there?  That's what I came up with too.   

Obviously, the odds on the first pull would be 10 to 1.

Multiply by 10 on the second pull and it's 100 to 1.

Multiply by 10 on the third pull and it's 1000 to 1. 

That's exactly the way it's figured; I just didn't bother spelling it out. (BTW, it's the same odds as drawing the Daily Number in PA, which pays 500-1. Cheap bastiches.)

[phattymatty]

how did you get that? 

if you go by the same logic from murp's question the answer would be 10,648,000 to 1 but i know that can't be right.

[Wingspan]

how many people at the table at the deal factors into it i believe

[phattymatty]

no that shouldn't matter at all.  there's still 4 of each card in the deck regardless if they're being dealt or staying in the deck.

[Susquehanna Birder]

But you're talking about drawing from a pool of available cards. If it's just you pulling from the deck, the first ace is a 1-in-52 chance. The second is a 1-in-51, and so on. But with other players at the table, the calculation gets a little more complicated because you have to assume whether they have drawn aces or not, as well.