Possibility vs. Probability?

Question

Is there a logical difference between possiblity and probability?

When the term 'odds' is used, is that refering to "possiblity" or "probability", or does it have its own unique definition?

When the term 'chance' is used, is that refering to "possiblity" or "probability", or does it have its own unique definition?

Using the Powerball lottery as an example, is there a difference between the possiblity and the probability of the numbers 1 through 6 being drawn (in exact numerical order)?

I've argued that the POSSIBLITY of 1 through 6 being drawn in exact numerical order has the same POSSIBILITY as any other numbers being drawn in any order ... but that the PROBABILITY of 1 through 6 being drawn in exact numerical order is much lower then any other numbers being drawn. Am I right or wrong?

Answer 1

Possibility and probability mean exactly the same thing, except that possibility is not a terminology used in math.

On your last question, you aren't phrasing it precisely enough. The probability/possibility/odds/chance of drawing 1-2-3-4-5-6 is exactly the same as the probability/possibility/odds/chance of drawing any other single specific ordered set (i.e., 1-2-3-4-5-6 has the same exact odds as 6-5-4-3-2-1 or as 2-3-5-1-6-4). But if you say 1-2-3-4-5-6 has a lower probability of being drawn than ANY other, well, of course it does--any one specific order has a fair lower odds than all of the other possibilities.

So, what I mean is, the odds of drawing them in numerical order is 1/21; the odds of drawing them in reverse numerical order is 1/21; the odds of drawing them in the order 1-5-3-2-4-6 is 1/21; the odds of drawing in something OTHER THAN numerical order is 20/21.

Answer 2

In statistical terms a possibility is any event whose probability is greater than zero. p(X) = 0 means event X is impossible. So whether you talk of "odds" or "chances", that is usually about probability. A "possibility" is anything that has a chance of happening, however small.

Take the experience of flipping a coin. The two possible events are heads and tails, each having probability 50%. Any other event has probability 1 - 50% - 50% = 0, and is therefore impossible. That's the theory. In practice, there might be a possibility that a coin might land on its edge and stay there. It is possible, but its probability is so small as to be negligible and for all practical purposes we say it's impossible. We can even make it impossible by rigging the experience: instead of saying "toss a coin and look at the result" we can say "toss a coin and if the coind lands on its edge, then bang on the table so that it will either fall on heads or tails."

Now, to your Powerball example. Drawing 1 through 6 is definitely a possible outcome. But if you do the math, you can also see that its probability is the same as any other combination being drawn. True, it is very small. But equally small is the chance of your picking six numbers at random, and winning the jackpot with these six random numbers.

What happens in Powerball is that you seldom see apparent "patterns" in the winning numbers because there are very few combinations with these apparent patterns (consecutive numbers, numbers having identical digits, etc.) compared to the numerous combinations that "look random". This leads to the fallacy that any particular combination that has a pattern (like consecutive numbers) is less likely to happen that another particular commbination, and that is why many players make elaborate but futile attempts to somehow "randomize" their picks.

We humans tend to be suspicious of random processes that give equal chance to results that seem nonrandom... There is also the example of a statistics professor who actually began his course by asking half the class to flip coins 100 times and writing down the results on a sheet of paper. The other half of the class were asked to write down fake results (no flipping coins). Then the result sheets were shuffled and handed to the prof, who successfully identified the fake ones from the real ones with an astonishing success rate (over 90%). His method: any result that contained a string of 6 consecutive, identical flips (six straight heads or six straight tails) was likely to be random. The probability of this happening in 100 consecutive coin tosses is pretty big. On the other hand, a student faking coin tosses would usually not throw in such a sequence because it seems too improbable at first glance. The students faking the results overdid their attempt to inject apparent randomness into their sequence.

All this being said... imagine what would happen if, one day, the numbers 1-2-3-4-5-6 really did turn up. I'm sure there would be a big to-do in the press, and suspicion of result-fixing on the part of the lottery agency. Yet every week, some equally improbable combination comes up, and nobody makes a fuss about "Mrs. Smith picked the combination 3-15-17-31-38-42 which had only 1 in 14 million chances of being drawn!!! How come she won? There must be a conspiracy!"

Answer 3

It is possible to give birth to a baby boy but the probability is 50%.

'Possibility' tells you if something can happen or not. 'Probability' tells you how many chances that event has to happen.

'Odds' and 'chance' are basically they're referring to probability.

It is possible to draw the numbers 1 to 6 in exact numerical order (because the logic tells you that) but the probability can be determined using mathematical formulas.

You're right. The possibility to draw any numbers, either in numerical order or not, is the same.

You're wrong. The probability of 1 to 6 being drawn in exact numerical order is the same as of 6 random numbers being drawn in any order. For instance, if we buy two different tickets (your numbers being 1 2 3 4 5 6 and mine 6 23 29 31 39 42), we have the same chances to win. That means the probability for your numbers to be drawn is as high (or low) as for my numbers being drawn.

Answer 4

Formally the difference between the words is that probability refers to the statistical odds of something happening while possibility simply means that it might happen. But when it is used as an idiom and we say that is more of a probability than a possibility, we are misusing probability to mean probable. The idiom means that something is more likely to happen than not.

Answer 5

Possibility is a "Yes" or "No" question. Yes, that is possible. Or no, it isn't possible.

Probability refers to the possibility of one outcome *relative* to all of the possible outcomes.

Chance refers to probability. Hence a 40% chance of rain, or a 1-in-6 chance of rolling a 2 on a die.

Answer 6

Possibility is the entire universe of everything that can happen. Probability is the likelihood that one or more of those possibilities will actually occur.

Answer 7

possible is if there is a chance for one thing to become true.
probable is more likely to be impeccable than to be true.

Answer 8

Jeremy Johnson and Nicki Roberts posted the same question. You should read the answers side by side.

Answer 9

Extremely good question, hope we get some good answers