statistical question

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flint
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statistical question

Post by flint »

I took statistics my senior year in high school and again 2 years ago in college but apparently not much stuck with me

what is the probability of having a boy followed by 3 girls (50% chance of having either sex)
if youre gonna be dumb you gotta be tough
shiram wrote:heh seeing as how the only other members we've seen in bathing suit are, iirc, Lisa, and mac...

so yea

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Post by Bane »

You know, the funny thing is I've studied alot of statistics (I'm studying for a master in economics) but apperently not much stuck with me either :D
I guess it's not as easy as 0.5^4=0.0625? Hell, after every exam I just make a complete memory swipe of everything I've learned and moves on to the next course, lol.. :mrgreen: Sometimes I can't even remember which courses I did last term, heh.
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Post by RoamingMadness »

.0625

its 50% on each child, regardless of sex

50% on the first one to be a boy
50% of THAT 50% will be a girl (which is 25% overall)
50% of THAT 50% will be a girl (which is 12.5% overall)
50% of THAT 50% will be a girl (which is 6.25% overall)

Understand?
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Post by flint »

yea I just figured there would be something more to it

ie you just found the probability of having 3 girls and 1 boy, shouldnt it be even rarer to have 3 girls and 1 boy in a specific order?
if youre gonna be dumb you gotta be tough
shiram wrote:heh seeing as how the only other members we've seen in bathing suit are, iirc, Lisa, and mac...

so yea

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Post by RoamingMadness »

That is in a certain order. Believe it or not..

The odds of just having 3 girls and a boy in any order is 12.5%, because any one child can be either sex.
You may say that I'm a dreamer
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Post by Bane »

Anyone recognize this?

AnB, A|B, AuB

I believe we used those to calculate probabilities. Lol, my brain is such a mess of useless shit, but all the good stuff just fades away, heh..
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Post by Styrofoam »

flint wrote:yea I just figured there would be something more to it

ie you just found the probability of having 3 girls and 1 boy, shouldnt it be even rarer to have 3 girls and 1 boy in a specific order?
roam is correct...... .5*.5*.5*.5

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Post by Mikeyrat »

Lets look at odds like this in the case of winning the lottery. I had a discussion one day with a guy who insisted that if the chances of winning the lottery were 1 in 10 million, by buying 10 tickets, his chances (odds) were then 1 in 1 million, reducing the odds against him by a factor of 10. But I insist that by buying 10 tickets, his odds simply become 10 in 10 million. He insisted that if he bought 1000 tickets, his odds would be 1 in 1000, which sounds a WHOLE lot better than 1000 in 10 million.

I also tried to convince him that the odds of the winning ticket being 1,2,3,4,5,6 were the same as it being 7,12,19,23,31,38 but he also scoffed at the idea. I admit there are a larger number of combinations where the numbers aren't in a series, meaning a non-series combination is more likely, but still the odds of a SPECIFIC serial combination are the same as ANY SPECIFIC non-serial combination.

/discuss
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Post by Styrofoam »

Mikeyrat wrote:Lets look at odds like this in the case of winning the lottery. I had a discussion one day with a guy who insisted that if the chances of winning the lottery were 1 in 10 million, by buying 10 tickets, his chances (odds) were then 1 in 1 million, reducing the odds against him by a factor of 10. But I insist that by buying 10 tickets, his odds simply become 10 in 10 million. He insisted that if he bought 1000 tickets, his odds would be 1 in 1000, which sounds a WHOLE lot better than 1000 in 10 million.

I also tried to convince him that the odds of the winning ticket being 1,2,3,4,5,6 were the same as it being 7,12,19,23,31,38 but he also scoffed at the idea. I admit there are a larger number of combinations where the numbers aren't in a series, meaning a non-series combination is more likely, but still the odds of a SPECIFIC serial combination are the same as ANY SPECIFIC non-serial combination.

/discuss
not much to discuss...the guy is an idiot, bottom line....which is how the lottery sucks people in, and wastes their money. Each ticket has a 1:100million chance to win.... so, you buy 10, and you OBVIOUSLY have a 10:100million chance. to win. You have 1:100million to win, ten times. Its the uneducated morons that think they can reduce the fraction by 10x if they buy 10 tickets. That's like saying if you buy 2 tickets, you cut your odds of losing in half! What a dumbass. Buying 1 million tickets will reduce your odds to 1:1million (you actually have to buy a factor of 10 to reduce it by a factor of 10) I feel sorry for this guy...really i do. as far a the 123456 and 2, 9, 12, 38, 45, 1 winning...the odds are exactly the same for any two specific numbers to appear - and while the odds for a sequential 6 digits to appear are lower, since there are far many more non-sequential number choices than sequential ones (123456 234567 345678 ... 45-46-47-48-49-50) any two random sequences chosen have the same probibilty of being chosen at random... strangely enough, this is the biggest misunderstood fact in lotto playing. I've NEVER heard of anyone playing 123456, or whatever. Its just unheard of.... but that ticket has the same chance of winning as any other single ticket in the country. Again, that guy is an idiot, and the sole reason i was against the lotto... it feeds on the ignorant and poor.

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Post by shiram »

yea gotta agree with styro here
he pretty much said it all
Yeah, well, you know, that's just, like, your opinion, man.

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Post by Mikeyrat »

I heard someone say the lottery was a tax on the mathematically-challanged.
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Post by StormCrow »

or a boon to the exponentially lucky :D

if you got an extra buck, might as well give it to them college kids in the off chance you win.

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Post by RoamingMadness »

If i have a bag with 100 marbles in it. And one of them is black. The odds of pulling out a black marble are 1 in 100.

If i have two black marbles in the bag, the odds are 1 in 50.

Does anyone know the odds if i have 4 black marbles in a bag of 200?

Write 4 out of 200 on your math test, PLEASE. PLEASE FOR THE LOVE OF GOD. I want to watch the teacher ask you if you attended classes in 5th grade.

The odds of 1 in 10, and 10 in 100 are the EXACT fucking thing. The only 'difference' is that one of them is for designed to make things easier to translate to other intelligent people. And the other is what stupid people use who don't understand the former.

If you buy 10 lottery tickets, you'll win 10 times more often, BECAUSE YOU'll BE PLAYING 10 TIMES MORE OFTEN. The only reason it doesn't fucking worth like that is because.. oh wait. It does work like that. I guess mikey is just retarded.

The second part is roughly debatable. But ultimately, ill agree. Same odds of 1, 2, 3 as 50, 2, 81.

Very, Very bad.
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Post by Kadian »

If you ask me your odds are always 50-50, either you win or you don't, now lighten up!

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Post by Mikeyrat »

RoamingMadness wrote:If i have a bag with 100 marbles in it. And one of them is black. The odds of pulling out a black marble are 1 in 100.

If i have two black marbles in the bag, the odds are 1 in 50.

Does anyone know the odds if i have 4 black marbles in a bag of 200?

Write 4 out of 200 on your math test, PLEASE. PLEASE FOR THE LOVE OF GOD. I want to watch the teacher ask you if you attended classes in 5th grade.

The odds of 1 in 10, and 10 in 100 are the EXACT fucking thing. The only 'difference' is that one of them is for designed to make things easier to translate to other intelligent people. And the other is what stupid people use who don't understand the former.

If you buy 10 lottery tickets, you'll win 10 times more often, BECAUSE YOU'll BE PLAYING 10 TIMES MORE OFTEN. The only reason it doesn't fucking worth like that is because.. oh wait. It does work like that. I guess mikey is just retarded.

The second part is roughly debatable. But ultimately, ill agree. Same odds of 1, 2, 3 as 50, 2, 81.

Very, Very bad.
The problem I see in your reasoning, and the reasoning of the fellow I was talking to is that you are still reaching into a pool of 100 marbles to pull out one. By putting two marbles in there, you aren't making two pools of 50 marbles with one black marble each... the pools are mixed, making it 2 marbles in 100 as opposed to 1 in 50. If you look at it that way, then you have to factor back into the equation the reality that you don't know which pool of marbles you'll be choosing from. A black marble in pool A is still competing with a black marble in pool B over which pool the pick will come from.

I dunno. Without some real math in the discussion, these things are hard to visualize.

I did some research, and found that the fundamental difference here is odds versus probability. They're not the same. Here is a simple post/answer from a mathematician:

http://experts.about.com/q/Probability- ... y-odds.htm
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Post by Genie »

Take this in a different perspective.
Are you calculating the chances of finding said black marbles in the case of fractional statistics or numerical statistics.

In the case of a fraction, yer chances of pulling a marble would be a 1/50 chance, having 2 marbles in a run of 100 total.

Now in the numerical instance, you would have a 2 in 100 chance. You can NOT fractionalize this because there isnt 50 marbles with one being black, you have 100 marbles. The chances of pulling a black marble are greater, because out of 100, 2 of them are black and 98 are white, but you'd have to sift through 98 white marbles to hit one of 2 black ones. Thats what numerical valued statistic is.

Now, in case of the buying 10 lotto tickets to the buying one; to throw another wrench into the pile. When you purchase a ticket, you increase the number of TICKETS overall. So now its 10 million and 10. Adding to the total number of tickets increases the statistic ratio; instead of having a 10 in 10 million chance (Numerically) you would have a 10 in 10 million and 10 chance, increasing the overall statistic. This is why winning the lottery is a lot less about statistical win and more on luck. Plus you'd have to factor in the number of variable sequences and a ratio of those 10 million tickets would have that exact sequence, meaning more than on winner.

Did I help this arguement any? I hope I hope.

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Post by RoamingMadness »

Mikey- Did you even read that 'simple' question you linked?
If your boss was right - 1 in 14M, 2 in 7M, 3 in 3.5M
And if whoever wrote this wasn't a dumbass, they might have a point.

Each ticket you buy doesn't cut the number in half. Only buying the second one does because you're DOUBLING the chances of winning. Lets use 14M as an example for a minute.

1Tix- 14M
2Tix- 7M
3Tix- 4.66M
4Tix- 3.5M
5Tix- 2.8M
10Tix- 1.4M

Notice that in order to cut your odds in half, you have to play twice as many tickets.

The odds of pulling out a black marble dont change at all.

If the bag contains 2 white marbles, and 2 black marbles, its a 50/50 shot. And if the bag contains 2000 white marbles, and 2000 black marbles, the odds don't swing either way, just because the numbers are bigger. Yet you insist they are. I hate to tell you this.. okay that's a lie, but you are very, very wrong.
You may say that I'm a dreamer
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Post by RoamingMadness »

Genie wrote:Take this in a different perspective.
Are you calculating the chances of finding said black marbles in the case of fractional statistics or numerical statistics.

In the case of a fraction, yer chances of pulling a marble would be a 1/50 chance, having 2 marbles in a run of 100 total.

Now in the numerical instance, you would have a 2 in 100 chance. You can NOT fractionalize this because there isnt 50 marbles with one being black, you have 100 marbles. The chances of pulling a black marble are greater, because out of 100, 2 of them are black and 98 are white, but you'd have to sift through 98 white marbles to hit one of 2 black ones. Thats what numerical valued statistic is.
Big deal, you're just giving things fancy names. It doesn't change the odds, and that is all that matters.

Now, in case of the buying 10 lotto tickets to the buying one; to throw another wrench into the pile. When you purchase a ticket, you increase the number of TICKETS overall. So now its 10 million and 10. Adding to the total number of tickets increases the statistic ratio; instead of having a 10 in 10 million chance (Numerically) you would have a 10 in 10 million and 10 chance, increasing the overall statistic. This is why winning the lottery is a lot less about statistical win and more on luck. Plus you'd have to factor in the number of variable sequences and a ratio of those 10 million tickets would have that exact sequence, meaning more than on winner.
Lottery tickets don't work that way. The odds aren't based on how many people buy tickets, its based on the odds of hitting your numbers. The odds ALWAYS stay the same to hit your number. If you want to throw wrenchs at something, talk about how the value of your dollar goes down the more you play. The Vaule of buying one ticket is far, far better than buying 10,000 tickets because only a percentage of each ticket sale goes into the jackpot. Not the whole thing. You could also consider the fact that the bigger the jackpot gets, the more people play, and because of this the odds of having to split the jackpot goes up very quickly. So you could argue that it might be better.. VALUE wise to play at 200 million instead of waiting till it hits 300 million.

None of that though, has to do with the odds. Which, no matter how you spin it, double when you play two tickets instead of one.
You may say that I'm a dreamer
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There probably isn't any meaning in life. Perhaps you can find something interesting to do while you are alive. Like how you found that flower. Like how I found you.

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Post by Mikeyrat »

RoamingMadness wrote:
Genie wrote:Take this in a different perspective.
Are you calculating the chances of finding said black marbles in the case of fractional statistics or numerical statistics.

In the case of a fraction, yer chances of pulling a marble would be a 1/50 chance, having 2 marbles in a run of 100 total.

Now in the numerical instance, you would have a 2 in 100 chance. You can NOT fractionalize this because there isnt 50 marbles with one being black, you have 100 marbles. The chances of pulling a black marble are greater, because out of 100, 2 of them are black and 98 are white, but you'd have to sift through 98 white marbles to hit one of 2 black ones. Thats what numerical valued statistic is.
Big deal, you're just giving things fancy names. It doesn't change the odds, and that is all that matters.

Now, in case of the buying 10 lotto tickets to the buying one; to throw another wrench into the pile. When you purchase a ticket, you increase the number of TICKETS overall. So now its 10 million and 10. Adding to the total number of tickets increases the statistic ratio; instead of having a 10 in 10 million chance (Numerically) you would have a 10 in 10 million and 10 chance, increasing the overall statistic. This is why winning the lottery is a lot less about statistical win and more on luck. Plus you'd have to factor in the number of variable sequences and a ratio of those 10 million tickets would have that exact sequence, meaning more than on winner.
Lottery tickets don't work that way. The odds aren't based on how many people buy tickets, its based on the odds of hitting your numbers. The odds ALWAYS stay the same to hit your number. If you want to throw wrenchs at something, talk about how the value of your dollar goes down the more you play. The Vaule of buying one ticket is far, far better than buying 10,000 tickets because only a percentage of each ticket sale goes into the jackpot. Not the whole thing. You could also consider the fact that the bigger the jackpot gets, the more people play, and because of this the odds of having to split the jackpot goes up very quickly. So you could argue that it might be better.. VALUE wise to play at 200 million instead of waiting till it hits 300 million.

None of that though, has to do with the odds. Which, no matter how you spin it, double when you play two tickets instead of one.
As I said Roam, we're talking about the difference between "odds" and "probability" which are two different forumlae. "Odds" in your book is

TOTAL TICKETS divided by NUMBER BOUGHT.

But the mathematical equation for probability, which is the ACTUAL LIKELYHOOD of the event occuring is:

1 - NUMBER BOUGHT divided by TOTAL TICKETS.

So in your marble analogy, 100/2 = 50 for the odds of 1 in 50 versus 100/1 for the odds of 1 in 100.

Probability, though, is 2/100 = (1-).02 = .98 , while 1/100 is .01 or .99. As you can see by doubling the number of chances doesn't double the "probability".
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Post by Styrofoam »

scroll down to the bottom, roam is right.

http://members.cox.net/mathmistakes/rawdata.htm

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