Things to pounder: The plane crash site

[Observer]

In John Irving’s book "The world according to Garp" one of the protagonists buys himself a house that was a former plane crash site. He does this because: "The chance that a second crash occurs on the same place is so much smaller"

This has always puzzled me.

I clearly understand that, purely mathematically, the chance that the same event happening on the same place is indeed 50% smaller.
So it looks like Garp's plan is a good idea
However: Nothing changed in the situation that there are still planes flying. There is only one plane less. In reality Garp is not much safer then he was before.

Some thoughts about random events (like plane crashes or seeing the same rare car twice a day)

Random events don't happen like you picture them in your mind.
Try the following amazing experiment if your bored.
Create a grid
Go to this electronic dice site
Throw once: this is your vertical number
Throw twice: this is your horizontal number
Tally-mark the corresponding cell
repeat until you have drawn 200 marks

Now...
If you look closely you’ll notice that some cell's seem to attract more outcome then others. Strange... are those cells blessed?

This phenomenon is called "grouping phenomenon" and is a driving force in nature. Variation in evolution can to some extend be explained by this phenomenon.

It becomes even better when you start working with averages
I am not lying when I say that "In Belgium, the average level of snow on Christmas day last 20 years is 1 cm"
Does that mean we always have a white Christmas here? No. It means we had 1 year with 20 cm of snow the last 20 years" mostly we have rain on the 25th

It’s all fun when it's about dice and tally-marks, but it becomes a hideous monster when it’s about emotional stuff, like plane crashes, cancer, or birth defects.

Any thoughts?

[mysticjbyrd]

"I clearly understand that, purely mathematically, the chance that the same event happening on the same place is indeed 50% smaller."

Nope, there is still the same chance assuming nothing has changed.
If the probability of me making a free throw is 50%, and I make my first shot, then the probability I make the 2nd is not 0%. Its still 50%.

[Stark Raving]

(23-11-2011 09:08 AM)mysticjbyrd Wrote:  "I clearly understand that, purely mathematically, the chance that the same event happening on the same place is indeed 50% smaller."

Nope, there is still the same chance assuming nothing has changed.
If the probability of me making a free throw is 50%, and I make my first shot, then the probability I make the 2nd is not 0%. Its still 50%.

Exactly. The irony in Irvings story is that buying a house on a plane crash site doesn't decrease the chances of a plane crash.

[Observer]

(23-11-2011 09:08 AM)mysticjbyrd Wrote:  "I clearly understand that, purely mathematically, the chance that the same event happening on the same place is indeed 50% smaller."

Nope, there is still the same chance assuming nothing has changed.
If the probability of me making a free throw is 50%, and I make my first shot, then the probability I make the 2nd is not 0%. Its still 50%.

Hmmm...
even=crash odd=no crash
I throw
could be even could be odd
50%

I throw twice
even odd no crash
odd even no crash
odd odd no crash
even even crash
25%= 50% of 50%
right?

[Stark Raving]

But you are making the outcome contingent on two throws. If you do, then you are correct, you're odds are 25% to hit odd/odd. But it's 25% to hit odd/odd every time you perform the experiment.

[Observer]

EDIT: misformulation

(23-11-2011 09:16 AM)The_observer Wrote:  I throw twice
even odd 1 crash
odd even 1 crash
odd odd no crash
even even 2 crashes
25%= 50% of 50%

---

(23-11-2011 09:21 AM)Stark Raving Wrote:  But you are making the outcome contingent on two throws. If you do, then you are correct, you're odds are 25% to hit odd/odd. But it's 25% to hit odd/odd every time you perform the experiment.

You are right...
I misformulated

[kineo]

(23-11-2011 09:16 AM)The_observer Wrote:  

This gif wins you one internet for today. o_ರೃ

[lucradis]

Not to mention the varying factors as to the original plane crash. Was it along a still trafficked route? Was the pilot drunk or was it mechanical failure? Did the airline if it was mechanical failure up their standard for competency? If they didn't the outcome remains as possible if not more likely it will happen again. I'd move. I think the hobbits had it right.

[houseofcantor]

The hell happened to the evil clown?

Probability.

As the creators of future, we are the dice of god; and we'll crash our planes anywhere we damn please.

[TheBeardedDude]

Runways are for suckers and mainstream pilots.


And people (like the character in this book) have a very hard time understanding what probability really means. It is like that scene in Dumb and Dumber.