Statistics question for the math people (1 Viewer)

[David Norman]

At one time I used to be decent math and basic statistics, but 40 years have diminished my reasoning power and it's driving me crazy that
I can't figure out why my answer makes no sense.

Basically the art of the unlucky.
A bag full of 40 different numbers picked one at a time and the drawn number is not replaced (2nd draw has 39 numbers, 3rd draw 38 numbers, etc), what is the probability that the #1 will be the very last number drawn

Or variation 40 marbles -- 39 red, 1 white. Odds that the white marble will be the last marble left.

The best number I can come up with is 39!:1, but that seems far too unlikely -- 40! different combinations numbers) with 1/40 of all the combinations with a specific item in the last slot

 

[DaveF]

I think it’s:
Prod(1-1/n), n=40…2

(1-1/40)*(1-1/39)*(1-1/38)*…*(1-1/2)*

Which is 1/40

Product[1-Divide[1,n],{n,2,40}] - Wolfram|Alpha

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www.wolframalpha.com

 

[DaveF]

1/39! Is the odds of picking a specific sequence exactly in order.

You want the odds of picking anything but one specific value, as the pool of options shrinks.

 

[Sam Posten]

The vast majority of people have an above average number of legs

 

[BobO'Link]

42

 

[David Norman]

Thanks. That was the first answer I came up with and it just didn;t feel right that 2.5% of the time it would take all 40 picks to get the specific item so I talked myself out of it. The other answer however seemed even more outlandish

Oh well, just goes to show what happens when you think too hard about things.