chance and cause

[sandy_mcd]

Why don't you explain all of this to me then? I asked you what chance was, and what causal powers it has, you did not answer.

Consider people flipping coins. The cause of the coin flipping is their thumb. By flicking the thumb against one face of the coin, spin is imparted and the coin will usually land on either heads or tails. It is most likely that if one knew all the parameters involved, it would be possible to calculate which face the coin lands on. Nonetheless, for a normal person doing a reasonable number of flips, it will be found that the results of coin tossing follow what is referred to as the laws of chance. The laws of chance give the probabilities of various outcomes. They neither affect nor effect the outcome. If a coin is tossed a large number of times, the number of heads and tails will be approximately equal. If heads predominates, the odds that the next toss will be tails is still 50:50; each toss is a separate event unaffected by the distribution of past tosses.
So if a coin is tossed a huge number of times and always ends up heads, the best explanation is that it is a two-headed coin. If not, there will most likely be some other trick or manipulation involved. Nevertheless, if a normal coin is tossed 1 million times and comes up heads every time, it is still finitely possible that it is just random chance. The cause is still whatever flips the coin. The outcome is chance. There is no way to predict what any individual outcome will be but given a large number of trials the approximate distribution can be predicted. I know that doesn't really explain chance but it is the best I can do.

Question: You have a class of 30 students, 15 coins, 15 pencils, 15 sheets of paper, and 1 hour before recess. You are assigned this problem: Design a coin toss experiment which is most likely to have results which are exactly half the time heads and half the times tails. What do you tell the students to do?

[August]

I don't have a long answer, just what I stated before. "Chance", in this context, is a formal statement referring to mathematical possibilites, i.e. it is a pure abstraction.

I don't think we differ much on this, reading your post above. I guess what I reacted to was the statement that we cannot distinguish between God and chance, and that puts chance on the same level as God, as a cause.

[BGoodForGoodSake]

Question: You have a class of 30 students, 15 coins, 15 pencils, 15 sheets of paper, and 1 hour before recess. You are assigned this problem: Design a coin toss experiment which is most likely to have results which are exactly half the time heads and half the times tails. What do you tell the students to do?

Set aside two of the most industrious students.

Have 14 student take a pencil each and have a pencil fight championship.

Have 14 more students each take a peice of paper and build paper airplanes.

Then taking the couple of industrious students, have them take a stack of 4 coins and arrange them head tail head tail on top of each other. Then instruct them to wrap this stack of coins tightly in paper. Have one student toss it to the other, carefully unwrap the stack and tally the results, on the remaining sheet of paper.

Pocket the last 11 coins.

=D

[sandy_mcd]

Showing off his intellect, Bgood came up with a simple solution with a 100% guarantee of success. The best I could do was 50%.
First, the number of tosses has to be even; otherwise there is no chance of 50:50.
If two kids each toss one coin, the chances are 50% that the final distribution will be exactly half heads and half tails. Any number of tosses other than 2 will have a lower chance of success.

[BGoodForGoodSake]

Showing off his intellect, Bgood came up with a simple solution with a 100% guarantee of success. The best I could do was 50%.
First, the number of tosses has to be even; otherwise there is no chance of 50:50.
If two kids each toss one coin, the chances are 50% that the final distribution will be exactly half heads and half tails. Any number of tosses other than 2 will have a lower chance of success.

Exactly right Sandy.

=)

Add two more tosses and your chances become 6 in 16.
See results below.

H H H H
H H H T
H H T H
H H T T HIT

H T H H
H T H T HIT
H T T H HIT
H T T T

T H H H
T H H T HIT
T H T H HIT
T H T T

T T H H HIT
T T H T
T T T H
T T T T