see Answer
see Answer
see Answer
see Answer
Drew Smith - Instructor, School of Library and Information Science, University of South Florida, Tampa has accumulated 700 points.
Points on this battle were won as follows:
It looks like there would be a 7% chance that all are white.
Here are the results:
1,000,000 Trials
13,988 times 10 white balls drawn
10 white balls drawn 1.40% of the time.
Number of 10 white total
Black balls balls drawn trials % of white % total % white
0 1016 1016 7.26 0.10 100.00
1 3499 9913 25.01 0.99 35.30
2 4635 43947 33.14 4.39 10.55
3 3276 116348 23.42 11.63 2.82
4 1283 205513 9.17 20.55 0.62
5 247 246244 1.77 24.62 0.10
6 32 204524 0.23 20.45 0.02
7 0 117809 0.00 11.78 0.00
8 0 44094 0.00 4.41 0.00
9 0 9653 0.00 0.97 0.00
10 0 939 0.00 0.09 0.00
totals 13988 1000000 100.00 100.00
Here is the program:
10 KEY OFF:CLS
15 DIM M(10),X(10),Y(10)
90 F=0
95 RANDOMIZE TIMER
100 FOR Z=1 TO 10:IF RND>=.5 THEN M(Z)=1 ELSE M(Z)=0:F=F+1
110 NEXT
115 Y(F)=Y(F)+1
200 W=0:FOR Z=1 TO 10:P=INT(RND*10+1):IF P<1 OR P>10 THEN STOP
210 IF M(P)=1 THEN W=W+1
220 NEXT
300 C=C+1:IF W=10 THEN X(F)=X(F)+1:X=X+1
400 LOCATE 1,10:PRINT C,X,USING"#####.##";100*X/C:Z2!=0:Z1!=0:Z3!=0
410 LOCATE 5,1:FOR Z=0 TO 10:PRINT Z,X(Z),Y(Z),
411 IF X>0 THEN Z2!=X(Z)/X
412 IF C>0 THEN Z1!=Y(Z)/C
413 IF Y(Z)>0 THEN Z3!=X(Z)/Y(Z!)
414 PRINT USING"#####.##";100*Z2!;100*Z1!;100*Z3!
415 NEXT
420 X$=INKEY$
450 IF C=1000000! OR X$=CHR$(27) THEN GOTO 600
500 GOTO 90
600 OPEN "BALLS.TXT" FOR OUTPUT AS 1
610 PRINT #1,STR$(C)+" Trials"
620 PRINT #1,STR$(X)+" times 10 white balls drawn"
630 PRINT #1,"10 white balls drawn ";:PRINT #1,USING"#####.##";100*X/C;
632 PRINT #1,"% of the time."
634 PRINT #1," ":PRINT #1," "
650 PRINT #1,"Number of ","10 white","total"," % total "
652 PRINT #1,"Black balls","balls drawn","trials","% of white black % white"
660 FOR Z=0 TO 10:PRINT #1,Z,X(Z),Y(Z),
670 Z1!=0:Z2!=0:Z3!=0
680 IF X>0 THEN Z2!=X(Z)/X
690 IF C>0 THEN Z1!=Y(Z)/C
700 IF Y(Z)>0 THEN Z3!=X(Z)/Y(Z!)
710 PRINT #1, USING"#######.##";100*Z2!;100*Z1!;100*Z3!
720 NEXT
900 CLOSE
1000 SYSTEM
Here is a mathematical solution:From: Aaron Dunn.
Maybe my understanding of probability is flawed, but it seems that the chances of there being ten white marbles in the box would remain constant regardless of the result of any ten random selections from that box. There should be no connection whatsoever between those two events. The probability of drawing ten white marbles from in a row will change based on how many white marbles are in the bag. But I don't think the results of the random selection should have any effect on the probability of having any particular combination of marbles in the bag (except for there being NO chance of having ten black marbles in the bag). I don't understand the point of the "simulation" you ran--perhaps it didn't factor in the random selection, but then what WAS the point? I do not know the math behind determining the solution to this problem, but it seems that it rests completely on the probability of flipping the coin ten times and getting ten heads in a row (and therefore only white marbles in the box). Maybe I am completely misunderstanding things here, and you never factored in the ten random selections from the bag, but I'm pretty sure that the answer to the question is determined as soon as the coin has been flipped ten times.
Reply from Duane:
We do not know how many white marbles are in the box but we are trying to determine that by the process of making ten random drawings. It is not that the random drawings affects the chances of there being ten white marbles. The number of white marbles, as you point out, is constant or predetermined based on the results of previous coin tosses. The point is that if we do draw ten white marbles, what can we determine about the chances that all the marbles are white. Obviously we can conclude that not all the marbles are black. We can also be pretty sure that there are not nine black marbles. We can be a little less sure that there are not eight black marbles, etc. Ordinarily one would think that if he drew ten white marbles in a row that if he drew an eleventh it would probably be white and therefore one might conclude that it is likely that all the marbles are white. But wait! We also know the process by which the marbles were originally chosen. Because of that we know that it is very unlikely that they are all white (actually about 1 chance in 1000). So taking the two probabilities together, the probability that the marbles actually are all white and the probability that we could draw ten white marbles in a row, what is the composite probability of these two events.
We find from the simulation that if we did draw ten white balls in a row the most likely situation is that there were actually eight white balls and two black balls in the box. There is a 33% chance of this situation vs. a 7% chance of ten white balls and a 25% chance of nine white balls.
War VII - battle 8
Points on this battle were won as follows:
War VII - battle 7
Points on this battle were won as follows:
P(366,26) = 366! / (366! - 26!) = 1.8e66 366^26 = 4.47e66 Probability = P(366,26) / 366 ^ 26 = 0.40The odds are actually a bit worse, since I assumed in the calculation that all 366 days have an equal chance of occuring, when Feb 29 only has a 25% chance of occuring. The break even point is about 22-23 people. With 23 people, the probability is 0.494%.
Points on this battle were won as follows:
As to what the Second Law *is*, Lambert describes it as "Energy spontaneously tends to flow only from being concentrated in one place to becoming diffused and spread out." As for entropy, Lambert says "Whenever energy flows from being concentrated to becoming dispersed, entropy has a positive sign mathematically and it increases. Therefore, over time entropy is constantly increasing because that's the direction energy flows in the real world -- toward diffusion."
As for curved spacetime, I bow to the words of "Sarfatti's On-Line Guide
to The Feynman Lectures on Gravitation"
(http://www.qedcorp.com/pcr/pcr/feynman/feyngrav.html), where the
following appears: "Asher Peres, in his recent textbook on quantum
mechanics (a la Bohr) shows that such a non-unitary theory permits
communication using Einstein-Podolsky-Rosen quantum correlations, and also
allows a Maxwell Demon to win, violating the classical limit of the second
law of thermodynamics."
See:
DIM A$(20) OPEN "R",1,"temp.txt",36 FIELD 1, 2 AS A$(1),2 AS A$(2),2 AS A$(3),2 AS A$(4),2 AS A$(5),2 AS A$(6),2 AS A$(7),2 AS A$(8),2 AS A$(9),2 AS A$(10),2 AS A$(11),2 AS A$(12),2 AS A$(13),2 AS A$(14),2 AS A$(15),2 AS A$(16),2 AS A$(17),2 AS A$(18) FIELD 1, 36 AS A99$ RESTORE FOR Z=1 TO 18:READ X:LSET A$(Z)=MKI$(X):NEXT PRINT A99$ CLOSE END DATA 28505,8309,25975,25970,24864,26400,28527 DATA 8292,24941,8302,26691,29281,25964,8307,25427,30056,31340,8225
Boy Meets Girl 1994
Burn Hollywood Burn 1998
With Sylvester Stallone, Whoopi Goldberg, Ryan O'Neal, Jackie Chan
Catchfire (aka Backtrack) 1991
With Dennis Hopper & Jodie Foster
Death of a Gunfighter 1969
With Richard Widmark
Dune 1984 TV version
Fade In (aka Iron Cowboy) 1968
Ghost Fever 1987
Hellraiser IV: Bloodline 1996
Since 1967 he has been credited with over 50 movies and TV shows. Who is
this, not so famous, director and when was he born?
Points on this battle were won as follows:
In 1904 an electrical engineer who had worked with Edison made use of the "Edison effect" and of the developing electron theory to devise an evacuated glass bulb with a filament and wire which would let current pass through in one direction and not in the other.
In 1906 an American inventor modified this device by introducing a
metal plate which allowed it to amplify electric current as well as
rectify it. This invention became the basis for many modern electronic
devices and changed the world. What was this invention called and
how was it used and who was the American Inventor?
see Answer
Michael A. Bayne - email: bayne@cs.virginia.edu
Zaheer Jhetam - gains 40 points for the correct answers to the questions below:
If binary 00010000 equals
10 hexadecimal equals
16 decimal
What is the product of
binary 00100001 and
binary 00000101?
Please give the answer in
binary, hex, and decimal.
Michael A. Bayne - email: bayne@cs.virginia.edu
Kady Gerry has 40 points for her answers to the questions below:
Drew Smith has 20 points for his answer to the question below:
Straight overhead the orb of noon
Beat down with brimstone breath:
The desert wind from south and west
Was blistering flame and death.
..............................
We feasted high there
And had much milk and meat.
The tables groaned to give us power
Wherewith to save the wheat.
Our beds were sweet alfalfa hay
Within the barn-loft wide.
The loft doors opened out upon
The endless wheat-field tide.
I loved to watch the windmills spin
And watch that big moon rise.
I dreamed and dreamed with lids half-shut,
The moonlight in my eyes.
For all men dream there
By noonday and by night,
By sunrise yellow, red and wild,
And moonrise wild and white.
The wind would drive the glittering clouds,
The cottonwoods would croon,
And past the sheaves and through the leaves
Came whispers from the moon.
Who wrote these words describing what place?
Question 1 was unanswered during War of the Minds II. The answer is:
The average circular tree spacing is 37 feet. Thus by A=pi*R^2 each tree takes up 18.5*18.5*3.14=1074.66 sq. feet. At 43,560 sq. ft. per acre there are about 40.53 trees per acre or 4053 trees on 100 acres. 4053 * (368 bd. ft. per tree) * $0.50 per bd ft. ($500 per 1000) = $745,800.
As for the quality of the stand 70 feet in height at 50 years of age is considered a good but not outstanding site index for Northern Red Oak. Remember the 70 feet is total height, not merchantable height. In a normal stand a yield of about 15,000 bd ft per acre as in this example would be reasonable at about 80 years of age. Foresters define a normal stand though not as an average stand but as an ideal stand, unlikely to occur in actual practice.
Drew Smith has 20 points for his answer to the question below:
Anne Lurie has 40 points for her answers to the questions below:
David Thomson has 40 points for his answers to the questions below:
Drew Smith has 20 points for his answer to the question below:
Ian Metcalfe has 20 points for his answer to the question below:
Drew Smith
says to also
see http://encarta.msn.com/index/conciseindex/17/0177D000.htm
and http://encarta.msn.com/find/concise.asp?z=1&pg=2&ti=03028000
Last revised May 12, 2000.
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