Re: Dice Program

GArlington wrote:
Having two dice with 6 sides (6 possible numbers each) how do you get
36 combinations?

Boris Stumm answered this one.

I can find ONLY 21 different combinations and ONLY 11 different sums.
So the probability of ANY particular combination is 1 in 21 and
probability of any particular sum is 1 in 11.

I don't know how you came up with 21, but most likely you are counting combinations (order doesn't matter) instead of permutations (order matters).

Most likely your assignment is to try to prove (or disprove) your (or
my) probability assumptions.

How are you coming up with a likelihood for that hypothesis?

Probability (as far as I remember from the long gone times when I was
a student) is something that works 100% ONLY in infinity, i.e. the
fewer attempts you make - the less likely you are to be close to what
probability is predicting.

I don't even know what you mean by that last sentence, but probability really doesn't have to do with infinity. Probability is the mathematics of expectation, and it works 100% even when there is only one trial.

Prior to a single coin flip, you can state unequivocally that the probability of either heads or tails is 50%. One coin flip.

Naturally the coin can only come up one or the other - it won't come up half heads. So after the fact (/a posteriori/, in the language of probability (and in Latin)), the probability of the observed outcome will be 100% - it was either heads or it was tails. Over larger sample size of /n/ coin flips, where n >> 1, the distribution of observed coin flips is expected to be close to half and half - the probability of a skewed distribution is lower the more skewed the distribution. So for 100 coin flips, the distributions with close to 50 each heads and tails are the most likely. Of course, a run of 100 heads (or tails) is still possible, just not as likely as 50-50. The probabilities involved follow Pascal's Triangle. Naturally, after the fact the probability of whatever was observed will be 100%, but we care about the /a priori/ probability - the odds of predicted future outcomes.

Regardless, the probability of heads on an upcoming 101st coin toss will still be 50%, whether the previous one hundred were all heads or not.

One way to calculate the probability for 100 heads in a row is to enumerate all the possible coin tosses, of which for 100 coins there will be the 100th power of 2 possibilities. "All heads" is only one of those, so the odds of seeing 100 heads in a row will be one out of 2 to the 100th.

The reasoning for dice is similar, except the odds are based on powers of six.

What are the odds that Wikipedia has a comprehensive set of articles on elementary probability?

--
Lew
.

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