Simple probability question

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?

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.

I agree with Doc. Excel gives 0.999999999999911.

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.

that it would *not* occur= 0.000000000000089

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

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.

1 in e^30 will get you close enough.

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?

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.
Crickets.

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.

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.

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.