What are the odds?

[TCDiver1]

Not the "odds" but the "probability." It's not the same thing. I don't claim to know the answer as i hated & almost flunked probability & sadistics.

The "odds" may be 1000 to 1 on any single day, but i think the "probability" of that number hitting on that specific day, on the one year anniversary is much, much smaller.

My guess:

1/1000 * 1/365 * ?? (one year anniversary)

Without the one year anniversary component i think the probability of this occurring is 365,000 to 1. Actually quite incredible if close to true. I think if the anniversary component is properly applied the probability of this happening would be much smaller

But what the heck do i know, that was a lot of years ago & i almost flunked the silly class.

 

[chrispete]

Never taken a stats class, but I'll give it a crack: Anytime you calculate odds for a single event (i.e. the lottery on a given day, whether you'll be sitting at an intersection when a beer truck flips over in front of you, etc.) the odds reset. When you flip a coin, there is always a 50% chance of it landing heads up - it doesn't matter whether you've flipped 100 heads-up in a row, there's still a 50% chance that #101 will be heads up. The same holds true for the lottery - the odds of the numbers 911 coming up had the exact same odds of coming up as 123 on that day because both were just as possible. The fact that the numbers match the date have no actual significance statistically because the chances are the same that on any day the pulled numbers will match the current date, your anniversary date, your birthday, your lucky number, etc...

 

[jonnythan]

nicodaemos once bubbled...
The odds are always 1000 to 1 for 9-1-1 to come up on any day of the year. We as humans like to put some significance to it, but from a statistical standpoint it's not unusual.

There was a point in my life where I would play the roullette wheel with the thought, what are the odds that after 10 reds in a row that it will come up red again? Well soon after losing my money I took a statistics class and came to understand why I lost. Turns out that they're always 50/50 minus the small percentage for the 0 and 00.

Not exactly.. the odds are 1/1000, .001, 0.1%, or 999:1. 1000:1 implies that the odds are 1/1001.

I was surprised the odds against it were so low. Can anyone explain, in layman's terms, how that is calculated?

Sure.. it's really not that hard. Say you have a coin. Odds are 1/2 that you'll get heads right? Well, say you do two flips. Odds are 1/2 that you'll get heads on the first flip and 1/2 that you'll get heads on the second. To get the odds that you'll get two heads in a row, you have to multiply the individual odds, since these are unrelated events. 1/2 * 1/2 = 1/4. So out of four pairs of coin tosses, you'll get one pair that's heads - heads.

Now look at the Pick 3 Lotto. There are three individual bins with tubes. Each bin has the balls 0 - 9 in them, and one ball is chosen from each bin. So what are the odds that we'll get a 9 from the first bin? 1/10. What are the odds that we'll get a 1 from the second bin? 1/10 (since the second bin still has ten balls). Odds that we'll get a 1 from the third bin? 1/10.

So on any given night, the odds of getting 9 - 1 - 1, in that order, from the series of bins is 1/10 * 1/10 * 1/10 = 1/1000.

These are exclusive events, so the denominators always stay the same. For something more complicated, think about getting a royal flush from a deck of cards. Since order doesn't matter, you can get *any* royal card or 10 first, right? There are twenty of these cards, so the odds of you getting one are 20/52.

Then once you have a 10 or face card, you're locked into that one suit. Say you got the Jack of Diamonds. The next card has to be the Queen, King, Ace, or 10 of diamonds. That's 4 cards, so the odds of you pulling one are 4/51 (notice that it's out of 51 since there's one less card in the deck).

Then there are three more cards you need, out of 50. Then two you need out of 49, then the last one out of 48.

So, the odds of getting a royal straight flush are:

20/52 * 4/51 * 3/50 * 2/49 * 1/48 = 480/311,875,200 = 1/649,740

So one hand out of every 649,740 will be a royal flush. Of course this doesn't take into account card drawing, but we're just talking about probabilities, not poker

To put this in another perspective, there are 2,598,960 possible poker hands. Only four are royal flushes.

To get the possible poker hands you have to realize you have 52 objects taken 5 at a time, and possible combinations are 52!/(5! * (52-5)!). Possible permutations would be far higher, but permutations take into account the order in which you draw the cards, which doesn't matter in poker.