Education

Roll the dice – answer the question

(c) Earl L. Haehl  Permission is given to use this article in whole as long as credit is given.  Book rights are reserved.

Here again to confuse your minds because tearing out loose cobwebs keeps you awake and active. I, myself, am learning Spanish (and unlearning Italian because they confuse one another) and studying some of the improvements in math I let by while being a bureaucrat. And you are unlucky enough to hear about it.

Did you all whip out your TI-83s to solve the puzzle. I hope not, because the answer is that on any roll of the dice there are six chances in thirty-six possibilities that the number seven will emerge. Each roll of the dice is a separate event.

Now the odds of there being 101 consecutive 7s are 101 in 3.919911741×10 to the 78th power. That is a whole lot of zeroes. But is can happen. And if you keep rolling the same set of dice it tends to happen because of wear on edges or corners. And if you’re Sky Masterson, it helps to sing “Luck be a Lady,”(1) What the odds say is that in a random world it doesn’t happen very often.

The other thing you can do with the dice is to have one person roll the dice for say a half hour to 45 minutes and another record the number that shows each time. Then look at the distribution to see if it resembles the pattern. If someone did several thousand rolls it would probably work out—to find subjects who would go through that much boredom without it phasing them you need ed psych majors—sorry but there are things a lab rat would not do.(2)

If the results do not correlate to the chart, just remember that statistics has never been an exact science and that there are always random variances. Normal people realize this. In college I had a set to with my biology lab instructor because my fruit fly counts did not match the ratios in the book so I handed him my covered petri dish and told him to have at it. When you’ve matched wits with a vice principal for six years a grad student in public health is not that intimidating. General rules do not govern specific cases.

A further discussion can result in some questions of the randomness of nature.
1. Why did the microburst only take out half of the Bradford pear and nothing else on the property?
2. According to Native American lore (or possibly pioneer lore since Native Americans have not said everything they’re alleged to), the City of Topeka was protected from tornadoes by the location of Burnett’s mound in relation to the Kansas River. Why did the 1966 Tornado come over Burnett’s Mound?
3. Does lightning strike twice in the same place?

Footnotes:

1. From Guys and Dolls, a Frank Loesser musical based on some short stories by Damon Runyon. Sky Masterson is a character based on WB (Bat) Masterson, a fellow sports writer with an interesting past.
2. The terms ed psych major, law student, lawyer and lab rat can be used interchangeably.

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Education

Logic & Statistics The Question

(c) Earl L. Haehl  Permission is given to use this article in whole as long as credit is given.  Book rights are reserved.

Okay, homeschoolers out there and those who want to play with numbers. Back when I was in high school I was what we call a nerd. Those questions in calc that require graphing the answer we used to do with a slide rule and graph paper. What is the secret to math and logic? It’s a game.

The simplest introduction to statistics is the craft of the bookmaker. The game of chance presumes a random order. And the fall of the dice on the green table is not dependent on who is betting or how much. The dice are simply cubes with dots on them. When they roll they must land on one of those sides or we’ve found ourselves in one of the Rev Mr Dodgson’s mathematical fantasies where they could as easily balance on a corner or not land at all. I prefer dice to coins because with 36 possibilities they hold the attention longer.

A logical question based on a legitimate statistic is as follows:

1. A standard die has six sides and the odds of it landing on any side if tossed is 1 in 6.
2. 2 dice each have the same independent odds of landing on any side. However, the odds of both landing on specific numbers in order to have a specified total is related to 6×6 or 36 possibilities.
a. 2 1+1 1 in 36
b. 3 1+ 2, 2+1 2 in 36, 1 in 18
c, 4 1+3, 2+2. 3+1 3 in 36, 1 in 12
d. 5 1+4, 2+3, 3+2. 4+1 4 in 36, 1 in 9
e 6 1+5, 2+4, 3+3, 4+2, 5+1 5 in 36
f. 7 1+6, 2+5, 3+4, 4+3, 5+2, 6+1 6 in 36, 1 in 6
g. 8 2+6. 3+5. 4+4, 5+3, 6+2 5 in 36
h. 9 3+6, 4+5, 5+4, 6+3 4 in 36, 1 in 9
I. 10 4+6, 5+5. 6+4 3 in 36, 1 in 12
j 11 5+6, 6+5 2 in 36, 1 in 18
k, 12 6+6 1 in 36
3. The most likely number to be thrown (barring weighted dice) will be 7. The odds are still against any specific number being thrown.
4. To decide what the odds of throwing any lot of 7s you add the top numbers in the top and multiply the bottom. So for the odds on two in a row are 1+1/6×6 or 2 in 36.
5. The question is: Randy has rolled 100 7s in a row. Presuming this to be random and not the result of funny dice odds of this occuring 100 in 6.533186235 x 10 to the 77th power.

. Now 10 to the 77th power is 1 followed by 77 zeros—they have a way to represent it, but not a name.  Realize that looking at those zeroes can give you one heck of a headache. This is a number for use in statistics or quantum physics. So what are the odds when Randy picks up the dice again that he will roll a 7?

THE ANSWER WILL BE POSTED ANON

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