| Sunday,
August 24, 2003 On
the Probability issue:
The probability in the juror problem should be p =
1.37931E-09 or .00000000137931
Solution:
The first 45 jurors (Pool A) get picked and the first
trial ends without a decision. Then juror # 46 is selected. He has a 315/360
chance of not being from pool A. The next juror has a 314/359 chance of not
being in pool A. (314 non-pool A people are left out of 359 total people)
The next has a 313/358 chance, and so on until 271/316.
After the second trial ends unsuccessfully, a 91st
potential juror is chosen. By now, only 270 "unused" jurors are available
from the pool of 360, so the probability of this person being "new" (not
from pool A or pool B) is 270/360. The next has a probability of 269/359
followed by 268/358 and so on until 216/316.
The event for which we are seeking the probability for
is that ALL of the selected jurors are new to the case and so the final
probability is found by multiplying ALL of the 90 individual probabilities
together. I used a spreadsheet and a lot of Fill Down commands to get the
answer above.
The answer is so small because we are always
multiplying the running product by a Positive number less than one. It makes
this problem similar to the question about how many people should be in a
room before I bet money that at least two share the same birthday. (The odds
are in favor of at least one shared birthday when 23 people are together.
When 41 people are tested, the odds are over 90% for at least two people
sharing a birthday.
Think of it as the evil twin to compound interest to
understand the shape of the curve...
Dave Coffland
Precisely.
I'm not a mathematician, but I've
learned a few things about random selections.
The reader who sent in the question about making
selections from a pool 360 of potential jurors made the usualy "common
sense" mistake most people make with regards to random selections -
particularly things like state lotteries. Most people think if you flip a
coin 50 times, and it comes up "heads" 50 times, then it must be more likely
that the next flip will come up "tails". Which isn't true. Each coin flip
result is completely independent of the previous flip.
In each case, selecting 45 jurors from the pool, the
chances of a single, particular juror being chosen (at random) is 1 in 360.
When you select the 2nd juror, it's 1 in 359, etc...
When you do the new selection (and put the original 45
back in the draw), everyone has exactly the same chance of being selected
again.
And, of course, the same is true for the 3rd
selection.
Like a state lottery, the outcome of the previous draw
has no effect on the outcome of subsequent draws.
So how unlikely is it that none of the 1st selection
of 45 were selected again in the 2nd selection, or 3rd selection? The answer
should be "exactly the same as the chances that any single one of them would
be chosen again" - and therefore should be irrelevant to the trial, since no
bias in the selection exists.
If you want to prove that the selection process is
biased (ie that the original 45 weren't properly returned to the pool for
re-selection) you won't find the proof in statistics.
And, if you're foolish enough to waste money on a
state lottery (stupidity tax), then why not use the numbers "1-2-3-4-5-6",
which have exactly the same chance of winning as any other selection.
Charles
A couple of points. The gambler's fallacy is that
independent events are not independent: that is, in a truly random series,
the next event has the same odds as the last. However, if the wheel seems to
favor red, bet red: it may not be a true roulette wheel, and the same with
dice. That is events may not actually be truly random or truly independent.
That, however, is not what was happening here.
=================
The problem with having a strong point of view is
that you stop analysis; as witness:
Date: Aug. 24,
2003
subject: The Near East
Dear Jerry:
Certainly they are biased. Look at some
quotes:
"The Pentagon, the US military and
American analysts are reluctant to acknowledge popular support for the
Iraqi resistance. But the chaos has tribal sheiks, Baghdad businessmen and
many ordinary Iraqis speaking in such harsh anti-American terms that it is
hard not to conclude there is a growing body of Palestinian or
Belfast-style empathy with the resistance. . . .
"If the accounts of the resistance given to the Herald in
interviews in the past 10 days are accurate, US intelligence is way behind
understanding that what is emerging in Iraq is a centrally controlled
movement, driven as much by nationalism as the mosque, a movement that has
left Saddam and the Baath Party behind and already is getting foreign
funds for its bid to drive out the US army."
Except the article doesn't site much evidence
of popular support. Ordinary Iraqis complain? When in any country with
free speech don't you find people complaining? As
the article I
sent you the link for the other day shows, there are plenty of people
who report lots of support for us among Iraqis. In this respect, it's
worth noting that "Ahmed" in the SMH article talks of
opposition from Muslim "jihadis," both Iraqi and
foreign. I think the SMH is projecting what they want to see into their
reporting.
It's also worth noting that Arab culture is
one of shame & honor. They routinely lie about their strength, their
enemies strength, & what happened in battle, all for the purpose of making
themselves look stronger and more successful than they are. See
this story for examples (it may no longer be available, but I'll mail
you a copy if it isn't and you want it). See also
Ralph
Peter's recent column in the NY Post for an argument that the
opposition is losing, badly.
On Israel, I'm rather puzzled by your
statement: "I see
Israel has ended the Road Map. Now I am not fixing blame and don't shoot
the messenger: but the Road Map is dead with the latest Israeli attacks on
Palestinian political leaders. When you kill the people you are
negotiating with, soon enough there will be no one willing to step forward
and say they are in charge, and if you can't find anyone to talk to it is
hard to make peace." It was the Palestinians that attacked
Israel, sending in several kamikaze bombers to kill Israeli civilians.
Are the Jews just supposed to take it?
Best,
Stephen
DELENDAM ESSE SAUDI ARABIA!
And that is about as silly as anything I can think
of.
Are they just supposed to take it? It depends on
what they want. What has what people are "SUPPOSED" to do with
strategy or results? The predictable result of attacking the Palestinian
leadership is that the leadership will go to ground, hide, and there will be
no one to negotiate with. The Brits can tell you something of that.
It may be the moral thing to do, to go attack the
leadership. It may be the moral thing to do, to go in and destroy a whole
block of middle class shops and cast formerly middle class Palestinians into
utter poverty. Perhaps they deserved it. Perhaps all Palestinians deserve it
since they don't stop the attacks. But I would myself find today's
Washington Post article a better guide to what to do if the desired result
is some kind of compromise and negotiated settlement.
Some results are predictable. They have little to
do with morality or "deserts" or what one is "supposed" to do. The US had
little choice but to make alliance with the USSR, and England had none at
all, back in World War II days; England actually contemplated war with both
Germany and the USSR over the invasion of Poland before sanity prevailed.
One defines ones goals, and the price one is
willing to pay. Israel hasn't defined a goal, in part because there is a
faction that will take nothing less than expulsion of the Palestinians from
all of Judea and Samaria, just as there is a faction of Palestinians that
will settle for nothing less than the destruction of Israel as a state. The
difference here is that the Palestinian goal isn't possible. The extreme
views of the settlers is at least in theory possible if they can manage to
get enough of the Israeli people behind that view.
What is not possible is any kind of stable peace
that leaves an indefensible line between Israel and Palestine. Long term
readers will recall that I long ago said if Israel wants peace, unilaterally
build a defensible fence, pay compensation to all the Palestinians on the
Israeli side of it, and ship them into the fenced off area. Then declare
that a state and hold it responsible for the actions of its citizens. But
the Fence they are building now encompasses too much or too little: it is
not a defensible line.
It may be that all the political leadership of the
Palestinians deserves death. It may be that all the political leadership of
the USSR deserved death. National strategy cannot always be governed by what
people deserve.
Like many, Mr. St Onge believes he KNOWS what must
happen, and thus if only he could get everyone to UNDERSTAND his view they
would accept it. I am pretty well familiar with the sources he gives, and
others as well. I have my own wishes about the Middle East. Wishing doesn't
make things so.
===
Are we looking at this from the wrong perspective?
Looking at the mid-east, or perhaps that should be
mud-east, or muddle-east, I'm inclined to wonder if we are putting our eggs
in the wrong basket. It is clear that there is never going to be, at least
in my lifetime or likely anytime in the next ten generations, anything
recognizable as "peace" within a couple hundred miles of Israel.
Part of this problem is Sharom and his compatriots.
Who really seem to feel that Hitler had the right basic idea, but simply the
wrong target group. A problem which they seem to have have corrected to
their satisfaction.
And part of this problem is Arafat, who claims to be
popularly elected, but as best I remember was a raghead terrorist in charge
of a group that also would have believed that Hitler had the right idea (had
they ever heard of him) but again the wrong group. A problem they have
corrected to their satisfaction.
As long as either of these people are alive and free
in that area, there will not, and can not, be any concept of peace. It would
be political death to either of them; and that is a death that is far worse
to them then the deaths of any tens of thousands of civilians and/or
supporters. So peace Will Not happen.
But, sitting here in America, I have to wonder. What
is that to us? I read the Constitution again today. As best I can make out,
it seems to imply that neither the People note the Federal Government are
responsible for the behaviour of Other States. And it seems to fairly
specifically suggest that the Various States themselves are denied this
power. So why do we care?
Well, one reason that I care at the moment is the
current world situation that seems to exist. For whatever reasons, there
seem to be tens of thousands of people that claim the only way they can
achieve Heaven is by killing me and anyone else residing in or associated
wiht America. One of the reasons these sort of people seem to give for this
belief is our support, or at least perceived (by them) support, for Israel.
A support which would seem to buy us very little,
morally, financially, or otherwise. Indeed, it is costing me dollars from my
pocket, as billions a year in US taxes are donated to Sharom to continue his
war. It is potentially going to cost me or my neighbors our lives if someone
with a backpack bomb walks up to us in the mall and blows us all up. And if
that doesn't happen due to the goodness of Our Government, it will be
largely because the final scraps of the Constitution have been burned on the
alter of Security.
I also don't see how we gain morally by financing a
decades-long war of attrition, which is carefully tailored to be below the
birth rate on either side, and can thus be a never-ending war. Of course, we
can claim to only be financing one side of the war, and that that side is
"defending" itself. As the other side can claim, with at least equal
justification.
Where is the benefit to the United States, or to the
people of the US, to finance the dessolution of our own Constitution, and
the active hatred of several million people (or perhaps it is, or will be,
several hundred million people) who believe the only way to heaven is
through our deaths? Wouldn't there be better uses for our tax dollars?
Building power plants, for instance?
Of course, at this point simply removing funding from
Israel would be of little use. It might result in Sharon and friends being
pushed into the sea in a couple of decades. Or it might result in them
deciding to nuke a ditch around the edge of the country and kill anyone
within the borders that can't show German heritage. Which would only
half-serve our interests: the taxes might (doubtfully) be slightly lower.
But it would only encourage those millions of heaven-seekers to come blow us
up; and would encourage the Government to finish eliminating the
Constitution For The Duration.
As I see it, our clearest interest as Citizens would
be served by finding a way to discourage, or perhaps dis-encourage, those
that feel they need to kill us for supporting Israel. This would then in
theory remove some of the need for zeal that the Government is seeking in
its need to repeal the Constitution. I see both of these results as
valuable.
I am personally rather unconcerned with the actual
fate of a few million Israelis and Palestinians who seem to have no life
ambitions other than death, as their goals are limited to the deaths of
themselves and each other. Perhaps some bible school might like to send
Missionaries to the heathen and change their goals over time. I do not see
that it is the business of the US Government to be those Missionaries.
I wonder what actions we could be taking that might
tend more to result in goals that would be useful to ourselves. It seems
that our current policies are demonstrably very unuseful to ourselves, and
of questionable benefit to much of anyone else.
Loren Wilton
My friend Ron Unz is concerned about the Israelis
but would like to have the US bomb what he calls "the crazy settlers" since
Sharon won't do it. I suspect he is not serious, but his view is that so
long as the crazy settlers have a veto there will never be peace.
My own view is that I really am weary of paying for
Israeli socialism through US aid. We are not paying Israeli defense costs:
we pay for socialism. I am not sure why we send $2,000 per Israeli citizen
per year, and smaller but quite significant amounts to Egypt, at a time when
we are running a deficit. I haven't found many willing to explain that to
me.
===================
Subject: Montana's population
Jerry,
One of your readers wrote:
"Did you know that Montana has 1/2 the population it
did in 1900? And that the Buffalo Grass Project is occurring at an
accelerated rate since the greeners forgot about it and everybody else but
Ted Turner left town? And that the buffalo used to cut communications
between the Coasts by scratching their backs on the telephone posts,
especially after Western Union put in spikes to stop them from doing that?
No, I don't live in Montana but I digress, as usual."
Well, I do live in Montana, and have since the early
sixties, and didn't leave town. The statistic that the population in Montana
had decreased by 1/2 since 1900 seemed suspect to me. Below is an excerpt of
the stats from the Montana Goverment website....and they indicate the
population has tripled, which was more in line with my thinking. Now, I
won't argue that during the gold rush, there was a significant undocumented
population, but I don't think it was hundreds of thousands, and that was
long before 1900, anyway.
Anyway, my point is Montana is very crowded now,
having four fifths of a million people in it. If you are from California or
New York, you wouldn't like it here. The people are crusty and hard to get
along with. You'd be much happy in Colorado or New Mexico. Trust me. :-)
http://ceic.commerce.state.mt.us/Demog/historic/Historicrace.xls
TOTAL
PERCENT
PERCENT PERCENT AMERICAN AMERICAN PERCENT
YEAR TOTAL WHITE WHITE BLACK BLACK INDIAN INDIAN OTHER OTHER
1880 39,159 35,385 90.40% 346 0.90% 1,663 4.20% 1,765
4.50%
1890 142,924 127,690 89.30% 1,490 1.00% 11,206 7.80% 2,538 1.80%
1900 243,329 226,283 93.00% 1,523 0.60% 11,343 4.70% 4,180 1.70%
1910 376,053 360,580 95.90% 1,834 0.50% 10,745 2.90% 2,894 0.80%
1920 548,889 534,260 97.30% 1,658 0.30% 10,956 2.00% 2,015 0.40%
1930 537,606 519,898 96.70% 1,256 0.20% 14,798 2.80% 1,654 0.30%
1940 559,456 540,468 96.60% 1,120 0.20% 16,841 3.00% 1027 0.20%
1950 591,024 572,038 96.80% 1,232 0.20% 16,606 2.80% 1,148 0.20%
1960 674,767 650,738 96.40% 1,467 0.20% 21,181 3.10% 1,381 0.20%
1970 694,409 663,043 95.50% 1,995 0.30% 27,130 3.90% 2,241 0.30%
1980 786,690 740,148 94.10% 1,786 0.20% 37,153 4.70% 7,603 1.00%
1990
799,065 741,111 92.70% 2,381 0.30% 47,679 6.00% 7,894
1.00%
Thanks
Tracy
The weather alone is enough to keep me out. My wife
inherited a share in a mine on the Montana Idaho border, and she was born in
the Idaho silver mining country. I have visited it once. I see why I
met her in Seattle, and we don't go up there much. But to each his own.
============================
Hello Dr. Pournelle:
I read, with great interest the free market
piece (
http://www.townhall.com/columnists/brucebartlett/bb20030814.shtml ),
that one of your readers kindly sent in. The piece is correct, as far as it
goes, but it does not go nearly far enough. His blinders are clearly shown
by the almost humorous statement that "The truth is that manufacturing is
doing just fine in every way except employment." Apparently the loss of
livelihood is just a minor detail. You have to admire the total lack of even
pretended interest in the human side of things that such a remark shows.
Here is a man who will go far in business.
He goes even further, by stating "The decline in
employment is, in effect, a good thing, because it means that manufacturing
productivity is very high." Well what a comfort that is to know. Such
statements are sure to help the self esteem and pride of the swelling ranks
of unemployed workers. It is interesting to note that the author's entire
career has been in government. I suppose this could count as a mitigating
circumstance.
Whatever it is that government produces, it
certainly does make it in large amounts. If we are five times more
productive, does this mean it is better to have four non-productive people
for everyone that produces? Even worse, do we think it is preferable to have
four out of five people released from the production workforce, in order
that two may become lifetime welfare recipients, while two others become
lawyers, government employees, or enter the service industries?
Whatever the situation, if the per capita income stays
the same, taxes stay the same, even if the income distribution changes; the
government gets just as much revenue. So perhaps to government
administrators, and advisors, like the author, it really makes no difference
how many people are working, or where the taxes come from, as long as the
overall amount is the same or greater. This would seem to reflect the
attitude that the only function of the economy is to support the government.
One comment on the free market, and the effects of
human greed. We are having the 100th anniversary of the founding of Harley
Davidson, this coming weekend, here in Milwaukee. Harley offered tickets for
$50 each, for the private events. Hundreds of thousands of people will be
coming. I got my tickets months ago; needless to say tickets are sold out
now. Ticket vendors are getting about $400 each for these $50 tickets. This
might not seem so bad, except that part of the reason there is a shortage,
is that months ago, ticket vendors, or their agents, bought up thousands of
tickets, and held them. Though I would regret the waste, I truly hope that
these people get stuck with these tickets. I suppose that in times past,
these people would have been production workers, but our newly efficient
productivity has freed them up produce nothing, inconvenience the rest of
us, and add to the cost of things. After all, they have to make a living
too. Welcome to the brave new world of the "service" economy.
Neal Pritchett
Better to speculate in Harley Tickets than to be
making motorcycles, surely?
Best regards
Dr. Pournelle: I agree with you that is very difficult
to assess the truth of this article linked below:
http://www.smh.com.au/articles/2003/08/15/1060936052309.html that
someone sent you on Friday. I could not even find the name of the reporter
listed. I have not read many articles form the Sydney Morning Herald
previous to this one, but a few quick glances at their web pages convinced
me that their editorial slant is definitely to the "left." That does not
automatically rule out the accuracy of the story, but it does put doubt in
my mind about unverified reports... James Casertano
I'll have my own views when I get back. Meanwhile,
I don't believe a lot of what I hear; but I do know that Bush is now down
below 50% popularity and if he isn't re=elected our Iraq policy is going to
change a LOT.
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