Tom's calculations indicate how hard it is for the human mind to grasp
probability, and thus why we cannot calculate risk properly.

Tom's coin analogy fails because he is looking for an unbroken sequence
of survival, which therefore takes into account the past in predicting
the future. His calculations are cumulative. Even with coin tosses, we
can see that once we ignore the past and stop cumulating results, the
calculation changes.

Thus, at the start of the week, the chance of survival for a week at
coin toss levels is 1 in 128. The chance of surviving for 8 days is
worse, at 1 in 256. However, if our subject survives day 1, his chance
of making day 8 increases to 1 in 128, and by the end of day 7 it has
risen to 50:50. The older he gets, the longer his chances of living
forever! I think (but as a European writing after what UK
government-sponsored has recently described as a "hazardous" level of
wine consumption I cannot be sure) this may be related to Zeno's paradox
(in Tom Stoppard's words, "... thus proving that the arrow never reaches
it's target and Saint Sebastian died of fright").

If we ignore the past, however, each day's chance is the same at 0.5.
Thus Ray (may he live forever) is able to state that next year his
chances will be pretty much the same, if he makes it that far.

Cumulation of probabilities is what the human brain does automatically.
Suppose the chance of being killed on a glider flight is 1 in 1,000. The
mind (without extensive training) deals with this in a number of ways:

1. I can fly safely 999 times, then have to give up or I will certainly
die on the 1,000th. If I'm already dead, I was "statistically" unlucky.

2. I've had 500 flights, so my risk level has risen to 50:50.

3. At my club we fly 1,000 flights a year between us, so one of us is
sure to die flying.

Unless I'm badly mistaken, none of these are true statements.

I try to think as follows:

a. In the UK where I fly, gliding fatalities are on average around 2.5
per annum out of 5,000 pilots, so my "statistical" risk is around 1 in
2,000 of dying through gliding each year.

b. I can do a number of things to reduce my personal risk to less than 1
in 2,000, so I'll try to do those things.

c. This is, to me, an acceptable level of risk for the pleasure I get
from gliding.

The good thing is that these probabilities are not cumulative. I've been
flying for 11 years, so if they were cumulative my "statistical" risk
might be down to under 1 in 20. It ain't.

What can be cumulative are personal mistakes - careless rigging, no
positive check, lack of sleep, etc. etc. These are the things I worry about.


Tom Gardner wrote:
On Nov 1, 2:11 pm, 1LK wrote:
The calculation which yields the 80/1 is only true for the single
instance;

Single instance of what? If it is the "single instance of a day",
then the calculations are correct.

my odds of being here next year are another thing entirely.
For that you need to do mortality computations.

To stay alive for a week, you have to toss "heads" 7 times in a row,
and the probability of that is 0.5 ^ 7 = 0.078125 = 1 in 128
It's not binary, it's multifactorial.

I don't understand: what do you mean by "it" and "multifactorial"?
Binary? Well yes, flipping a coin is binary; that's why I
subsequently
used your figures (that you didn't bother to include).

It might help if you could explain the reasons (based on an
equivalent
example, if you prefer) why you believe that the calculations are
wrong.
Examples I can think of are
- it is not a 1.25% chance of dying on every day, only on some days
- each day shouldn't be treated as independent from the preceding
days (but that doesn't fit with your original statement)

Anyway, I am glad that your mortality isn't as imminent as it
at first appeared.