Talk:Probability theory

in the explanation of sample space, shouldn't the word "sequence" be "combination" as the order of the Californian voters does not matter?

The article on probability theory is superficial. It uses jargon, while being disconnected from real life. I believe that the best foundation to theory of probability is laid out here:

[1]

The article is accompanied by free software pertinent to probability (combinatorics and statistics as well).

Ion Saliu, Probably At-Large

To give a mathematical meaning to probability, consider flipping a "fair" coin. Intuitively, the probability that heads will come up on any given coin toss is "obviously" 50%; but this statement alone lacks mathematical rigor. Certainly, while we might expect that flipping such a coin 10 times will yield 5 heads and 5 tails, there is no guarantee that this will occur; it is possible, for example, to flip 10 heads in a row. What then does the number "50%" mean in this context?

One approach is to use the law of large numbers. In this case, we assume that we can perform any number of coin flips, with each coin flip being independent—that is to say, the outcome of each coin flip is unaffected by previous coin flips. If we perform N trials (coin flips), and let N_H be the number of times the coin lands heads, then we can, for any N, consider the ratio ${\displaystyle N_{H} \over N}$ .

As N gets larger and larger, we expect that in our example the ratio ${\displaystyle N_{H} \over N}$  will get closer and closer to 1/2. This allows us to "define" the probability ${\displaystyle \Pr(H)}$  of flipping heads as the limit, as N approaches infinity, of this sequence of ratios:

${\displaystyle \Pr(H)=\lim _{N\to \infty }{N_{H} \over N}}$ 

In actual practice, of course, we cannot flip a coin an infinite number of times; so in general, this formula most accurately applies to situations in which we have already assigned an a priori probability to a particular outcome (in this case, our assumption that the coin was a "fair" coin). The law of large numbers then says that, given Pr(H), and any arbitrarily small number ε, there exists some number n such that for all N > n,

${\displaystyle \left|\Pr(H)-{N_{H} \over N}\right|<\epsilon }$ 

In other words, by saying that "the probability of heads is 1/2", we mean that if we flip our coin often enough, eventually the number of heads over the number of total flips will become arbitrarily close to 1/2; and will then stay at least as close to 1/2 for as long as we keep performing additional coin flips.

Note that a proper definition requires measure theory, which provides means to cancel out those cases where the above limit does not provide the "right" result (or is even undefined) by showing that those cases have a measure of zero.

The a priori aspect of this approach to probability is sometimes troubling when applied to real world situations. For example, in the play Rosencrantz & Guildenstern Are Dead by Tom Stoppard, a character flips a coin which keeps coming up heads over and over again, a hundred times. He can't decide whether this is just a random event—after all, it is possible (although unlikely) that a fair coin would give this result—or whether his assumption that the coin is fair is at fault.

The article starts with: "Probability theory is the branch of mathematics concerned with probability." By clicking on the last word, we learn that "Probability is the branch of mathematics concerning numerical descriptions of how likely an event is to occur, or how likely it is that a proposition is true." So, combining these two definitions, we now know that

Probability theory is the branch of mathematics concerned with the branch of mathematics concerning numerical descriptions of how likely an event is to occur, or how likely it is that a proposition is true.

This doesn't make sense. I think the two articles should be merged, and the term "probability" should not be defined as being a branch of mathematics.  --Lambiam 00:37, 8 February 2023 (UTC)Reply

Probality is the chance of an event to occur. Like if you roll a die, let's say you wan't to get a certain number. For example, if you want get a number, let's say, on a 6 headed dice, there will be a 1/6 chance. But it could also change based on how the die is shaped. A number could get closer and closer to a number, (As defined as a variable in my example) IF the probability is going to increase every time, but cannot reach a certain probability. Evergreen tenal (talk) 22:06, 13 February 2023 (UTC)Reply

Hat note at probability uses the wording "mathematical field of probability". Less redundant at least. Slywriter (talk) 22:26, 13 February 2023 (UTC)Reply

When editing the article yesterday, I completely forgot about the fact that die is the singular form of dice. I pondered why I rarely ever hear the term "die" compared to "dice" (hence me forgetting it exists) and decided to read up a bit on "dice vs die". From what I have gathered, die is the original singular form of dice, but dice has also become an acceptable singular form, especially in modern English (as stated in multiple online dictionaries). Does anyone have any opinions or further information on this matter? Wikipolym (talk) 08:57, 28 February 2023 (UTC)Reply

Personally, I am used to and prefer "die" as the singular form of dice, and an old discussion at the dice article displayed some statistics that pointed in favor of the usage "roll a die" vs "roll a dice". However, the same discussion has been resurrected from time to time at that article's talk page, with various people pointing out (as you noted) that OED and other dictionaries accept dice as both singular and plural. At this stage, I've finally decided to stand off from enforcing one vs the other, since it's clear what's being described in this article. But it would be ideal if there was uniform usage of "die" vs "dice" in the singular case on wikipedia.—Myasuda (talk) 14:13, 28 February 2023 (UTC)Reply