Statistics?

Question

When someone says there is a "one in thirty thousand chance" of whatever, exactly how do "they" determine that number. For ex.: just taking the number of people in the U.S., and the chances of getting struck by lightening, if it storms in one small area of the country, huge clusters of people aren't going to all drop dead from getting struck. So on a larger scale who really knows the real percentage of anything so random and large. (And please, I am curious but explain it in real-people language! ;-) Hee Hee) Thanks!!

Answer 1

As Mark Twain once said, "There are lies, damned lies, and statistics." ☺

When someone says the odds of something happening are 'one in thirty thousand' it's taken to mean that the expected event will occour (on average) once every 30,000 tries, twice every 60,000 tries, etc. But it says **nothing** about **when** in those 30,000 or 60,000 tries it will occur (this is called the 'distribution' of the event)

It is entirely possible that the first three tries will yield the expected result, and it won't happen again for 89,997 tries. This is *still* 1 in 30,000 odds ☺

I don't know the exact number, but let's say the chances of being struck by lightning are given as '1 in 50,000'. As a mathematician, my first question would be, "Is that one person struck for every 50,000 storms, for every 50,000 lightning strikes, or one person struck per 50,000 people?" You have to be **very** careful to understand how the statistic was calculated before it becomes meaningful.

Another thing that bothers a lot of people is that Nature has no 'memory' If you flip an honest coin, the odds of it coming up heads is 1 in 2. If you flip the coin 3 times in a row, the odds of it coming up heads all three times is 1 in 8 (half times a half times a half). Each time the coin is flipped three times constitutes a 'trial event'. If you have a few minutes, try it. Flip a coin 3 times and keep track of the number of times it comes up heads three times in a row and the number of total trials (and remember, it must be 3 flips per trial. If it comes up tails on the first flip, **do not** mark it down as a trial that didn't yield three heads and start the next trial. Flip it twice more) If you do this over a large number of trials (say 80 or more) you should see the ratio of 'all heads' to 'total trials' start getting close to 1 in 8 (in 80 trials, about 10 times you'll see 3 heads)

But here's something to think about. The odds of flipping 10 heads in a row are 1 in 1024. The odds of flipping 11 heads in a row are 1 in 2048. If you flip 10 heads in a row, what are the odds that the next flip will end up heads?

The answer is 1/2. Why? Because Nature has no memory of the last 10 flips. But why isn't it 1 in 2048? Because you've 'used up' the 1 in 1024 odds getting to 10 heads in the first place. Most people don't see this (and, as a result, a lot of gamblers make a *lot* of money ☺)

IN the real world, probability and statistics are very strongly math-oriented but, unless you're a 'mathophobic', you should be able to get through an elementary text on the subject. Or search the web for some sites that explain things in 'simple math' terms.

I hope that helped.

Doug

Answer 2

Building on Inferno's response, lightening strikes are reported to health bureaus, we know the population of the US, from this we can calculate the odds (adding a time component like Knowledge suggested would make it a rate). A one in thirty thousand chance is the same as saying one out of every thirty thousand people. But keep in mind some places are more prone to lightening storms, so the odds you mentioned are averaged and true odds really depend on where you live.

Answer 3

What u experience here is an hallucination of Statistics....Before we get into it let me first tell about how the calculate the chance....

its basic proobability where
chance = No of favourable events / Total no of possible events .

When expressed as fraction instead of percentage it comes out to what u say....
Suppose a die is rolled....we know that a die has 6 faces numbered 1 through 6. So what do usay is the chance of getting a 5.... it is 1 in 6...that is...the no of favourable event (getting a 5 ) is 1 out of the total possibilities of 6...sSo the chance of getting a five is 1 in 6...
Similarly the chance of getting a tail when a coin is tossed is 1 in 2 (if u ignore the possiblity of falling vertically upright :))
In ur case...the country takes a regular census of the population where they get the numbers from.... So if u say a prize is to be given to a citizen of the USA the chance that u will get it is 1 in .


What i previously meant by hallucination can be understood by the following example. Suppose there is a river with a depth of 4.5 feet. There is this person with his family who wants to cross the river (none of them can swim...they have to walk through)... Assume he is 6 ft, his wife is 5ft and his son is 4ft. Now the average height of the members is (6+5+4)/3 = 5ft while the depth of the river is 4.5ft.
So is it safe for them to cross..???.... Although statistically it is possible., while in reality the son would drown as he is only 4 feet while the river is 4.5ft deep !!!!!!

Answer 4

Well, I don't have any exact percentage to give, but using your figure of 1/30000 and lightning, for every 30,000 people in a group, 1 will be struck by lightning. There really needs to be a time period included. It could be 1 in 30,000 will be struck sometime in their lifetime, or per year, or by each lightning bolt.