Another math question (statistics?)
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Government Teat-sucker
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From: Virginia Beach
Another math question (statistics?)
Okay, guy on the radio (Glenn Beck) says that if you buy 140 million different powerball tickets, you have all the possible combinations covered. Now, it's been many years since I took algebra, but it seems to me that that number is quite a few short.
So, if you have a lottery that picks 5 numbers, with no possiblility of repeatiing numbers, and a powerball number, doesn't it work like this:
(Assuming you choose from 1-45) 45 x 44 x 43 x 42 x 41 x 40.
If so, there are at least 5 billion combinations available (5,864,443,200, to be exact). Please help me with this math. Maybe they are assuming a certain set of parameters, such as 6 consecutive numbers, or something... but that doesn't really make sense, because I've seen lottery numbers such as 10,11,12,13 before.
So, if you have a lottery that picks 5 numbers, with no possiblility of repeatiing numbers, and a powerball number, doesn't it work like this:
(Assuming you choose from 1-45) 45 x 44 x 43 x 42 x 41 x 40.
If so, there are at least 5 billion combinations available (5,864,443,200, to be exact). Please help me with this math. Maybe they are assuming a certain set of parameters, such as 6 consecutive numbers, or something... but that doesn't really make sense, because I've seen lottery numbers such as 10,11,12,13 before.
Post Fiend
Joined: Jan 2004
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From: Northwest, Arkansas
The odds of picking all 5 plus the powerball is 1 in 146.1 million. There was a group that tried this many years ago in order to win and it worked. I think they invested around 10 million to get back 30.
Now my luck would be to spend the 146 million to get the winning numbers and there would be 500 others that picked the right numbers.
Now my luck would be to spend the 146 million to get the winning numbers and there would be 500 others that picked the right numbers.
Postmaster
Joined: Jan 2004
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From: colorado
i just heard on the radio that the odds of winning are 147,000,000 to 1 so i would think there is 147,000,000 different combinations. the problem with that is if you won the jackpot and took the cash after taxes it would be about $90,000,000 (jackpot minus 60% minus taxes) and if you took the anuity you could make more on your original $147,000,000 than it would pay
Posting Guru
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From: just outside of Phila.
Think about it like this if you actually want to understand the math (I think this is the way it works for the lottery too...if I'm even right about this
).
Picture a keypad for a door, and it has a 2-digit code, and the numbers 1-9 and 0 are all available to use. This keypad will have 100 possible combinations to open the door. A 3-digit keypad will have 1,000. A 7-digit keypad will have 10,000,000 combinations that are possible, in other words, if you're just guessing, trying to unlock a 7-digit keypad, your odds of hitting it are 1 in 10 million. If you include # and *, then the number becomes 35,831,808 possible combinations.
Take the number of digits (10) and raise that to the nth power. So, 10 to the 7th power is 10 million, when n is the number of buttons you need to push.
I think that's right...math isn't my strongest subject. Speaking of, anyone understand Limits?
). Picture a keypad for a door, and it has a 2-digit code, and the numbers 1-9 and 0 are all available to use. This keypad will have 100 possible combinations to open the door. A 3-digit keypad will have 1,000. A 7-digit keypad will have 10,000,000 combinations that are possible, in other words, if you're just guessing, trying to unlock a 7-digit keypad, your odds of hitting it are 1 in 10 million. If you include # and *, then the number becomes 35,831,808 possible combinations.
Take the number of digits (10) and raise that to the nth power. So, 10 to the 7th power is 10 million, when n is the number of buttons you need to push.
I think that's right...math isn't my strongest subject. Speaking of, anyone understand Limits?
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Government Teat-sucker
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From: Virginia Beach
I know what the odds on the ticket say, but I still say there are over 5 billion possible combos... Like I said before, they must be assuming certain parameters, such as 2,4,6,8,10,12 as an impossibility, even though they aren't. What I'd like to know is if my formula is correct (when none of the numbers can be repeated).
As was stated above, if you have a 2 digit number, there are 100 possible combos (10x10, or 00-99). if the number can't repeat, then you have a total of 90 combos (10x9). Conversely, if it is a three digit number, that doesn't repeat, there should be 720 combos, right? (10x9x8=720). Is there another way to figure out the total when you have to pick 6 numbers out of 45?
As was stated above, if you have a 2 digit number, there are 100 possible combos (10x10, or 00-99). if the number can't repeat, then you have a total of 90 combos (10x9). Conversely, if it is a three digit number, that doesn't repeat, there should be 720 combos, right? (10x9x8=720). Is there another way to figure out the total when you have to pick 6 numbers out of 45?
Elder User
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From: Plano, Tx.
Originally Posted by stu37d
. . . if you have a lottery that picks 5 numbers, with no possiblility of repeatiing numbers, and a powerball number, doesn't it work like this:
(Assuming you choose from 1-45) 45 x 44 x 43 x 42 x 41 x 40.
(Assuming you choose from 1-45) 45 x 44 x 43 x 42 x 41 x 40.
45 x 44 x 43 x 42 x 41 = 146,611,080
but can't it repeat numbers? In which case the possible combinations would be
45^5 (45 x 45 x 45 x 45 x 45) = 184,528,125
EDIT: your calculations are right if six numbers are drawn
45 x 44 x 43 x 42 x 41 x 40 = 5,864,443,200 possible combinations
Last edited by woogs; Oct 19, 2005 at 02:46 PM.
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Posting Guru
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From: just outside of Phila.
No, the lottery doesn't repeat numbers, at least on these big jackpots. They do on the pick 4's and such though.
I don't remember how to do the whole 45 x 44 x 43 x 42.... on my calculator without it going all of the way down to 1, but woogs is right how he came up with 146 million. After 1 ball has been drawn, there are now 44 possible numbers that could show up. After another, then it becomes 43...so on and so on obviously.
EDIT: Then he's correct with 5 billion, because the BIG money doesn't come until you've hit the 5 number AND the Powerball, right?
I don't remember how to do the whole 45 x 44 x 43 x 42.... on my calculator without it going all of the way down to 1, but woogs is right how he came up with 146 million. After 1 ball has been drawn, there are now 44 possible numbers that could show up. After another, then it becomes 43...so on and so on obviously.
EDIT: Then he's correct with 5 billion, because the BIG money doesn't come until you've hit the 5 number AND the Powerball, right?
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Elder User
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You're almost right in the way you start out, but the statistical model requires you to stop at (n-k+1) and that the total be divided by the factorial of the sample (in this case, 6). See here for a thorough explanation
http://www.saliu.com/oddslotto.html
http://www.saliu.com/oddslotto.html
Elder User
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One night I was watching the news when I lived in Atlanta and this guy won 12 million bucks through the lotto and they asked him what was the first thing he was going to buy and he said " a doublewide and move back to Alabama"..
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I don't mean to veer off the stastistics subject, but I want to see if anyone shares my point of view. When the Powerball is at ~$1 million, even though the odds are much better, very few people buy a ticket. When it gets up to several million, people rush from all over the country to buy tickets, even though the odds are much less. $1 million would greatly change my life. I would be more likely to buy a ticket when the total is low, & have a better chance of winning, than when it is very high & have a 1 in 5 million chance. Does that make sense? Does anyone agree with me?