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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