Probability problem
Wed Aug 11, 2004 6:25 pm
Remember the thread about the NY lottery a while back? Well on the way home from work today for some reason I got probability stuck in my head. In the thread we talked about buying more than one lottery ticket and odds. The odds completely depend on independent trails versus specific number selection which is not independent trials. Look at the problem I have hypothesized below and tell me what you think.
We have a game. There are 100 numbers in a bin and we will draw one and that will be the winning number. One person buys a ticket for every number 1-100 so he is guaranteed to win. There is a 100% certainty he will win. The second person also buys 100 tickets but instead of buying 1 for each number he lets the lottery machine randomly pick a number for him 100 times. This is the difference between non-independent trials and independent trails.
I hypothesize that person one will win, 100% probability.
Person two will be 63.4% likely to match the number and win. This is because we have a series of 100 independent trials each with 100:1 odds of winning. There will be duplications of numbers which is why the probability is only 63.4%. So any idea how I got 63.4%? I used a method of computation but am unsure if it is correct. Do you think I am correct or mistaken? I think I am correct but am not completely sure.
Sorry to be so incredibly geeky but occasionally I like these types of math problems.
Jim
P.S. I named you 3 guys in th subject line because I think you all voiced strong opinions in the thread. I am sure there were other people who thought they were right too.
We have a game. There are 100 numbers in a bin and we will draw one and that will be the winning number. One person buys a ticket for every number 1-100 so he is guaranteed to win. There is a 100% certainty he will win. The second person also buys 100 tickets but instead of buying 1 for each number he lets the lottery machine randomly pick a number for him 100 times. This is the difference between non-independent trials and independent trails.
I hypothesize that person one will win, 100% probability.
Person two will be 63.4% likely to match the number and win. This is because we have a series of 100 independent trials each with 100:1 odds of winning. There will be duplications of numbers which is why the probability is only 63.4%. So any idea how I got 63.4%? I used a method of computation but am unsure if it is correct. Do you think I am correct or mistaken? I think I am correct but am not completely sure.
Sorry to be so incredibly geeky but occasionally I like these types of math problems.
Jim
P.S. I named you 3 guys in th subject line because I think you all voiced strong opinions in the thread. I am sure there were other people who thought they were right too.
Wed Aug 11, 2004 6:34 pm
Let me guess. You must be a statistics major (if you are still in school). 
Not sure if this is the same comparison. My brain is starting to hurt so I will make this short.
Assuming the lottery is a combination of 6 digits, there must be a maximum amount of possible combinations. Let's just say for example this number is 3 trillion possible combinations (someone smarter than me may have the actual number). Obviously if you buy 3 trillion tickets with you handpicking all the different combinations, you would win.
But of course who wants to spend 3 trillion bucks to win 300 million?
Not sure if this is the same comparison. My brain is starting to hurt so I will make this short.
Assuming the lottery is a combination of 6 digits, there must be a maximum amount of possible combinations. Let's just say for example this number is 3 trillion possible combinations (someone smarter than me may have the actual number). Obviously if you buy 3 trillion tickets with you handpicking all the different combinations, you would win.
But of course who wants to spend 3 trillion bucks to win 300 million?
Wed Aug 11, 2004 6:49 pm
So the 2nd guy got a machine to randomly generate 100 numbers? What a bafoon.
Well, not being a math major, here is what I would think.
The moron who got the random numbers, besides from having a serious case of brain damage, would not have a good chance of winning.
Using my rudimentary knowledge of probability....
For every duplicate he gets, his odds of winning go down, but so do his odds of getting another duplicate.
I think his odds would be 50/50.
But, like I said, I have no mathematical background.
Well, not being a math major, here is what I would think.
The moron who got the random numbers, besides from having a serious case of brain damage, would not have a good chance of winning.
Using my rudimentary knowledge of probability....
For every duplicate he gets, his odds of winning go down, but so do his odds of getting another duplicate.
I think his odds would be 50/50.
But, like I said, I have no mathematical background.
Wed Aug 11, 2004 6:52 pm
Originally posted by CodeRed68
Let me guess. You must be a statistics major (if you are still in school).
No, I was not a math major. I had a math course in college about 20 years ago that covered probability. I think I am just either incredibly geeky or insane for even spending time thinking about statistical problems.
Jim
Wed Aug 11, 2004 7:26 pm
There's a thing out there... it's called "a life". I urge you all to get one too!
I got one awhile back and man, does it ever kick ass!
I got one awhile back and man, does it ever kick ass!
Wed Aug 11, 2004 7:45 pm
I would say 50%. If the computer randomly chooses 100 numbers from 1-100, it would pick 50 different numbers (in an ideal world). Each number has the same chance of being picked. There may be duplications but its still one number/one choice, so you lose a percentage (1%) for every duplicate. And you also lose a percentage from the numbers that aren't chosen at all. If all probabilities were added, would they not equal 50%? Maybe I should take a gander at my old stats book.
Wed Aug 11, 2004 8:24 pm
the number should fall at 66.7 or 66.6666666...
in a random draw the numbers will repeat. it is actuall a 1 in 3 chance or with three numbers in a hat you will draw 1, which is 3 in 9, 9 in 27,or 66.666 in 100
in a random draw the numbers will repeat. it is actuall a 1 in 3 chance or with three numbers in a hat you will draw 1, which is 3 in 9, 9 in 27,or 66.666 in 100
Thu Aug 12, 2004 1:07 am
It depends on how you look at it:
It's either 1% (for the wise)
or 63.4%, or more precisely .63396765872677049506938397342748
using the formula 1- (99/100)^100
It's too late to get into this, time for some sleep. Unfortunately I have to do this sort of crap every day.
It's either 1% (for the wise)
or 63.4%, or more precisely .63396765872677049506938397342748
using the formula 1- (99/100)^100
It's too late to get into this, time for some sleep. Unfortunately I have to do this sort of crap every day.
Thu Aug 12, 2004 1:45 am
Originally posted by RCglider
It depends on how you look at it:
It's either 1% (for the wise)
or 63.4%, or more precisely .63396765872677049506938397342748
using the formula 1- (99/100)^100
It's too late to get into this, time for some sleep. Unfortunately I have to do this sort of crap every day.
I want to hurt you all... very badly. Thanks for the headache smakers.
Thu Aug 12, 2004 7:51 am
Do you people really have this much time on your hands? 
Thu Aug 12, 2004 8:10 am
Originally posted by RCglider
It depends on how you look at it:
It's either 1% (for the wise)
or 63.4%, or more precisely .63396765872677049506938397342748
using the formula 1- (99/100)^100
It's too late to get into this, time for some sleep. Unfortunately I have to do this sort of crap every day.
That is what I came up with but I was not sure if my method was correct. I just wanted to be sure it was correct. The only practical application of probability I use is occasionally playing poker, blackjack, or boardgames that use dice. What do you do that you have to do this stuff every day?
Jim
Thu Aug 12, 2004 9:56 am
I love how people bitch about this making their head hurt, or questioning the amount of time one has.
Don't you ever want to use your mind for anything more than shoveling food in your cakehole and pushing it out the other end?
"Go back to sleep"
Don't mind me I'm just a bitter software developer
Don't you ever want to use your mind for anything more than shoveling food in your cakehole and pushing it out the other end?
"Go back to sleep"
Don't mind me I'm just a bitter software developer
Thu Aug 12, 2004 10:25 am
The moron who got the random numbers, besides from having a serious case of brain damage, would not have a good chance of winning.
Merg.... the 2nd Guy is not all that dumb really, he acutally is smarter than Guy 1, if you think of this in terms of roulette.
Why do you think people dont cover every single number with one chip? Because you may win 35 bucks, but you put out 37 bucks to win 35.
Now... if you put 37 dollars on a few different numbers, lets say 10, you have less of a chance of hitting that number... but now if you do hit your number, you are getting close to $130 for hitting your number, instead of $35.
If the question is lottery though, and there were only 100 numbers, and if there were 10 different winners, they each split the pot, Then guy one is still the dumbass, because while he did spend $100 on each and every number, what if 12 hits, and there are 4 other people that put thier $1 on 12? Then he is only getting $20 for his $100 investment.
MY POINT IS....
He does have a 100% chance of winning...... but his winnings may actually be on the negative side of things...
We all have a 100% chance of getting laid if you ask every single girl you meet at a bar, but wouldnt you rather spend your time and money on a certain few to hit the jackpot? Rather than go home with Bertha?
Thu Aug 12, 2004 11:02 am
Originally posted by Jim0322
That is what I came up with but I was not sure if my method was correct. I just wanted to be sure it was correct. The only practical application of probability I use is occasionally playing poker, blackjack, or boardgames that use dice. What do you do that you have to do this stuff every day?
Jim
statistics and reliability.
what were the strong opinions you spoke of?
Thu Aug 12, 2004 11:13 am
Originally posted by Baddreams
I love how people bitch about this making their head hurt, or questioning the amount of time one has.
Don't you ever want to use your mind for anything more than shoveling food in your cakehole and pushing it out the other end?
"Go back to sleep"
Don't mind me I'm just a bitter software developer
In the grand scheme of things, if i saw my life pass before my eyes and saw that i partook of such a thread i'd be embarrassed. I suppose Chaos theory and probablity were among the portions of your education needed to become that bitter software engineer.
Besides i do use my brain for something else. I try and find more and more ingenious ways of wasting time. How about you?:lol: