A math connundrum

[JBDuke]

Son #1 is still wrong, there is no expectation that things will even out later (no matter how many tosses "later" encompasses). Son #2 is correct that the large number principal simply states that over a large enough sample the anomaly does not get corrected, but rather becomes such a small part of the data that it becomes obsolete.

In the 900 of 1000 example, the expected outcome of the next 10,000,000 tosses is 5,000,000 heads. So if that occurs, we see a total of 5,000,900 heads in 10,001,000 tosses, or 50.004%. The mean of the observed data have now approached the true mean without in any way "evening things out" with more tails.

Something tells me that telling #1 son he is still wrong, but that his younger brother is correct is NOT going to bring harmony to the Evans household...

[jimsumner]

Jason,

Have you asked your math-wiz kids if there's a correlation between cinder blocks and college-basketball success?

[madscavenger]

Something tells me that telling #1 son he is still wrong, but that his younger brother is correct is NOT going to bring harmony to the Evans household...

Don't you mean melody? Harmony is when you don't remember the words. Of course, the is is defense is always the fallback, and in any case is already taken. That's your out. And actually, i think its going to have to be mine as well. The Stanford Marching Band ain't got nothing on me.

[Bostondevil]

I was trying to explain this concept to my brother-in-law who likes to go to Vegas. He never loses more than he can afford, but he does usually lose.

He argued that after a long string of heads, tails are "due". I maintained that no matter what went before, each flip of a fair coin is still 50/50. He asked, "What would you bet if I got 500 heads in a row?" And I said, "Heads." This answer blew his mind - why in the world would I bet heads? "Because after 500 heads in a row, I no longer believe it's a fair coin. But it could be, and if it is, the odds are still 50/50."

Another BS in Math here, plus Comp Sci, plus an MS in statistics, although not from Duke.

I have known in my life some very smart people, even ones who did well in math, who just do not 'get' probability.

[BD80]

I was trying to explain this concept to my brother-in-law who likes to go to Vegas. He never loses more than he can afford, but he does usually lose.

He argued that after a long string of heads, tails are "due". I maintained that no matter what went before, each flip of a fair coin is still 50/50. He asked, "What would you bet if I got 500 heads in a row?" And I said, "Heads." This answer blew his mind - why in the world would I bet heads? "Because after 500 heads in a row, I no longer believe it's a fair coin. But it could be, and if it is, the odds are still 50/50."

Another BS in Math here, plus Comp Sci, plus an MS in statistics, although not from Duke.

I have known in my life some very smart people, even ones who did well in math, who just do not 'get' probability.

Wonder if the casino owners "get" probability. Probably do.

[JNort]

Didn't we have almost the same discussion a few weeks ago? With red and blue colored balls?


http://forums.dukebasketballreport.c...ility-question

Ah it was marbles.

[Nick]

FYI, it's apparently not 100% certain that coins are 50/50.

[Bostondevil]

Wonder if the casino owners "get" probability. Probably do.

Maybe.

What I expect they do understand is that the Law of Averages says, in the long run, the house always wins.

[Indoor66]

Maybe.

What I expect they do understand is that the Law of Averages says, in the long run, the house always wins.

I will guarantee you that casino owners understand probability, law of averages and the law of large numbers. In years past, probably intuitively. In today's world, with casinos being run by bean counters and numbers men, there is no question.

[snowdenscold]

FYI, it's apparently not 100% certain that coins are 50/50.

I didn't know the 51/49 theory for the flipping, but I have been aware for awhile that the spinning experiment is highly biased.

Another fun bar betting scenario is to stack a typical beer glass (see below) on top of 3-4 inches of anything, and wager whether the height of the glass + pedestal you've made is more than the circumference around the top.

[BD80]

I didn't know the 51/49 theory for the flipping, but I have been aware for awhile that the spinning experiment is highly biased.

Another fun bar betting scenario is to stack a typical beer glass (see below) on top of 3-4 inches of anything, and wager whether the height of the glass + pedestal you've made is more than the circumference around the top.

Full or empty?

[jimsumner]

I didn't know the 51/49 theory for the flipping, but I have been aware for awhile that the spinning experiment is highly biased.

Another fun bar betting scenario is to stack a typical beer glass (see below) on top of 3-4 inches of anything, and wager whether the height of the glass + pedestal you've made is more than the circumference around the top.

Probably more fun after you've had a few.

[Jeffrey]

I've never been wrong. But I've been overruled a lot.

Well I ain't often right, but I've never been wrong.

[Jeffrey]

Son #1 is still wrong, ...

...., or, Dad #1 is still wrong.

[OldPhiKap]

Well I ain't often right, but I've never been wrong.

image.jpg

Just saw that while walking around . . .

[Jeffrey]

image.jpg

Just saw that while walking around . . .

I had one of those flashes,
I'd been there before... been there before.

[Turk]

Proof that such scores were more difficult to achieve back when we took the standardized tests.

I think this is true. My sons just got their SAT scores back (new version of the test) and I was surprised how high they were. Will have to look and see what the percentiles are. They each shattered the official Turk Vegas over/under line by about 180-200 points on the combined number.

[BigWayne]

I think this is true. My sons just got their SAT scores back (new version of the test) and I was surprised how high they were. Will have to look and see what the percentiles are. They each shattered the official Turk Vegas over/under line by about 180-200 points on the combined number.

They have yet again a new scheme now it seems, going back to 1600 max from the 2400 of the last few years.

If you are referring to pre and post 1995 differences, you can see the chart here and explain about back in the day when it was harder to get high scores after you walked through the snow to take the test.

[BD80]

They have yet again a new scheme now it seems, going back to 1600 max from the 2400 of the last few years.

If you are referring to pre and post 1995 differences, you can see the chart here and explain about back in the day when it was harder to get high scores after you walked through the snow to take the test.

Uphill. Into the gusting wind.

Both ways.

[Mtn.Devil.91.92.01.10.15]

They have yet again a new scheme now it seems, going back to 1600 max from the 2400 of the last few years.

If you are referring to pre and post 1995 differences, you can see the chart here and explain about back in the day when it was harder to get high scores after you walked through the snow to take the test.

Are you saying I can no longer use my stellar SAT score to impress chicks?

Curse you, millenials!