Chance

I would have given your second answer, but don't really see the distinction from your first. Can you give me an example that fits one answer but not the other?

That's why I got so confused.

In the first example I haven't put a qualifier on my sentence. So therefore it could apply to any sample size. Hence, if you had a counter with ten copies of that product on it, one is guaranteed to be faulty. That's clearly wrong, isn't it?

It is.

Perhaps the best way to explain it is in terms of flipping coins or rolling dice. Everybody knows coins and dices from their daily lives.

With this in mind, here's how to explain what it means that a product has a statistical chance of about 16.667% of failing. "Every time somebody takes the product, you figuratively roll a dice. If the dice shows a "6", the product fails. If it shows any number between 1 and 5, it works. Hence, in a large-enough population sample, ....."

Ah, that makes it so clear. I think I understand probability a bit better now. Thanks.

EDIT: Also, I'm curious... Why on Earth is this a featured thread?

Since somebody decided to feature this thread, let me polish my explanation to make it as clear as possible.

Here's what it means that a product has a statistical chance of about 16.667% of failing: Every time somebody tries the product, you figuratively roll a dice. If the dice shows a "6", the product fails. If it shows any number between 1 and 5, it works. Because the dice has no memory, the outcome of a throw cannot depend on the outcomes of earlier throws. But if you roll the dice often enough by having the product tried by a large-enough population sample, you will find that about 1/6th of the trials, or about 16.667%, have led to a failure.

I'm glad it's featured.

Many people have a misconception, I think, of what the odds are for something happening. I think that's because we let our emotions get involved in it, at least to some extent.

If you were gambling, and would win Only if the die did NOT land on, let's say 4, you would feel more and more sure the next throw would be a winer, if you repeatedly threw a 4.

In theory though, you could throw a 4 a hundred times in a row, and it won't effect the outcome of the next throw, since, as Thomas said, each event has no memory of the past.

This reminds me of this asinine show I watched the other day about bible codes, and how it predicts future events, kind of like a "find a word" puzzle.
The only argument the people who believed this crap could come up with was that "the odds of this happening is so great, it just can't be by chance."

Never mind that they were making these words and phrases by changing the rules of the game for every instance, like "this time we'll skip every, uh....third letter....or do it backwards and from a different direction."

Also never mind that you could find all sorts of "coded messages" in any book of a large size.

Re: Chance


The first clue is your use of the word 'statistic' which can represent one of two things. It can either be a calculated outcome after the observance of all instances of the event (number of kids born in 1970 who graduated high school by 1990, for example), or the calculation of an estimate of future events (a 10% chance of observing a failure in a manufacturing environment in the next batch of production).

In the first case, you calculate that 10% of the kids born in 1970 did not graduate by 1990. Each of those kids (outside influences aside) had a 10% chance of not finishing school.

On the other hand, if you're using the number as an estimate of a future event, you need to add a confidence interval around your estimate. The actual failure rate of the next batch may be anywhere within a range (10% +/- an error band around your estimate). The error band is determined by the sample size of your original observation.

Specifically, if the historical observed failure rate is 10% on a large number of units, then there is an approximately 10% chance that you will see one failure in the next 10 units of production. There is a closer chance that you will see 10% overall failures in a larger number of units.

Your example states that a certain product had a 10% chance of failing. Used one way, it means that 10% of those products failed. Used another, it means that one can assume that approximately 10% of future products will fail.