rdw4potus
rdw4potus
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March 27th, 2018 at 7:07:21 AM permalink
hey guys. I'm blanking on a simple probability question, and coffee intake isn't helping me reach an answer.

If an event has a 0.3% probability, what are the odds of it happening at least once in 10000 trials?
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Doc
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Chuckleberry
March 27th, 2018 at 7:10:52 AM permalink
I think it would be: 1-(1-.003)^10000

The calculator on my phone just rounds this off to 1.

For 1,000 trials instead of 10,000, I get 0.950436917.
Wizard
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Doc
March 27th, 2018 at 7:35:50 AM permalink
I agree with Doc. Excel gives 0.999999999999911.
"For with much wisdom comes much sorrow." -- Ecclesiastes 1:18 (NIV)
rdw4potus
rdw4potus
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March 27th, 2018 at 7:41:08 AM permalink
thanks Doc. I tried doing it in my head on the fly, got 1:200trillion, worried that my rounding and estimation were too severely flawed, went with "it's a severe longshot, worse than lottery odds" on my call & promised to follow up later with backup. Then I got scared of the numbers, because they're just so big (or little, depending on perspective) & ran here for help.

Some background: I have a customer who assigns a 0.3%/day probability to a workplace event. They claim that it hasn't happened in 27 years. I've been telling them that either the probability assigned is too high or they have an under-reporting issue.

Edit: Thanks Wiz!

re-edit: just an FYI - if edits happen within the same minute as an initial post, they do not appear to be tagged with the "last edited by" information. Not sure if that matters, but happened here & thought I'd point it out.
"So as the clock ticked and the day passed, opportunity met preparation, and luck happened." - Maurice Clarett
odiousgambit
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March 27th, 2018 at 7:42:45 AM permalink
that it would *not* occur= 0.000000000000089

1 in about 11,235,955,056,180 [trillions]
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Wizard
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March 27th, 2018 at 9:59:35 AM permalink
Quote: odiousgambit

1 in about 11,235,955,056,180 [trillions]



To put that in comparison, the probability of throwing 18 yo's in a row is 1 in 39,346,408,075,296,600,000,000.
"For with much wisdom comes much sorrow." -- Ecclesiastes 1:18 (NIV)
Ace2
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March 27th, 2018 at 10:01:53 AM permalink
1 in e^30 will get you close enough.
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Ibeatyouraces
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March 27th, 2018 at 10:05:05 AM permalink
Quote: Wizard

Quote: odiousgambit

1 in about 11,235,955,056,180 [trillions]



To put that in comparison, the probability of throwing 18 yo's in a row is 1 in 39,346,408,075,296,600,000,000.


Now, I know we like to joke about this, but what are the approximate odds that's it's actually happened on a craps table somewhere on earth since the days of the first craps game?
DUHHIIIIIIIII HEARD THAT!
DeMango
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March 27th, 2018 at 10:34:59 AM permalink
Quote: Ibeatyouraces

Quote: Wizard

Quote: odiousgambit

1 in about 11,235,955,056,180 [trillions]



To put that in comparison, the probability of throwing 18 yo's in a row is 1 in 39,346,408,075,296,600,000,000.


Now, I know we like to joke about this, but what are the approximate odds that's it's actually happened on a craps table somewhere on earth since the days of the first craps game?



If it happened at Caesars, it would have made the papers!
Kinda like The Captains 3 hour roll in AC.
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ThatDonGuy
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March 27th, 2018 at 6:50:50 PM permalink
Quote: Doc

I think it would be: 1-(1-.003)^10000

The calculator on my phone just rounds this off to 1.

For 1,000 trials instead of 10,000, I get 0.950436917.


Correct - "the probability of an event happening is 1 minus the probability of it not happening."

In this case, 1 minus the probability of it happening zero times in 10,000 trials.

As for roundoff error, the probability of it not happening in 10,000 trials is (997/1000)10,000, which is 1 / ((1000/997)10,000), which, according to LibreOffice, is about 1 / 11,179,358,502,534.
sodawater
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RS
March 27th, 2018 at 7:14:43 PM permalink
Quote: Ibeatyouraces

Quote: Wizard

Quote: odiousgambit

1 in about 11,235,955,056,180 [trillions]



To put that in comparison, the probability of throwing 18 yo's in a row is 1 in 39,346,408,075,296,600,000,000.


Now, I know we like to joke about this, but what are the approximate odds that's it's actually happened on a craps table somewhere on earth since the days of the first craps game?



0.

Having 200 years of craps with thousands of tables doesn't move the meter at all when you're talking about this large of number.

A similar situation is that no fairly shuffled deck of cards has ever been identical in human history.
RS
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March 27th, 2018 at 8:58:13 PM permalink
If you roll the dice for every time you play a hand of VP.....you’d expect to get a dealt royal flush THREE times in a row.....143,000 times.....for every time you get 18 yos-in-a-row. IOW: 3 dealt RFs in a row would be 143,000 times more likely.

Correct my math if it’s broked.
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