From: wallace@dtc.hp.com (David Wallace)
Subject: Re: stats help
Date: Tue, 29 Dec 1992 23:38:35 GMT
Organization: Hewlett-Packard Design Technology Center, Santa Clara, CA

In article <BzzvrB.KCD@mentor.cc.purdue.edu> poutsmaj@mace.cc.purdue.edu (unknown) writes:
>I have a question regarding basic probability theory:  (I'll use baseball
>terms because that's what I'm using)  Suppose I have two teams EXACTLY
>equal to each other such that, when they play, the probability of either
>team winning is .500000 etc.  If they were to play, say, 1620 games (10
>seasons) against each other, what is the probability that they will each
>win exactly half?  What would be the distribution of possible outcomes?
>If I have two teams that play and each win half, what is the probability
>that the two are exactly equal ?  Any insight you can give me to this 
>problem would be helpful (I realize that this is probably elementary 
>probability theory, but that was one math class I never had).
>
>thanks bunches
>paul

Here is a portion of the output from my Titan hit calculator, set up to
answer your question.  This program calculates the probability distribution
of the total number of hits given various numbers of attacks each with
a (potentially) different probability of hitting.  For your problem, I set
# of attacks = 1620, prob of success = 0.5.  In your case, you should read
"wins" for "hits," but it's the same problem.  The second column gives the
probability of exactly that number of hits (wins), the third column gives
the probability of at most that number of hits, and the fourth column gives
the probability of at least that number of hits.  Give a cigar to the
poster who estimated the probability of exactly 810 wins at 2-3%: the
correct answer is 1.98%.

Dave W.

Hits    Prob    P(<= Hits)    P(>= Hits)
750     0.0002  0.0015        0.9987
751     0.0003  0.0018        0.9985
752     0.0003  0.0021        0.9982
753     0.0004  0.0025        0.9979
754     0.0004  0.0029        0.9975
755     0.0005  0.0034        0.9971
756     0.0005  0.0039        0.9966
757     0.0006  0.0045        0.9961
758     0.0007  0.0052        0.9955
759     0.0008  0.0060        0.9948
760     0.0009  0.0069        0.9940
761     0.0010  0.0080        0.9931
762     0.0012  0.0091        0.9920
763     0.0013  0.0104        0.9909
764     0.0015  0.0119        0.9896
765     0.0016  0.0135        0.9881
766     0.0018  0.0153        0.9865
767     0.0020  0.0173        0.9847
768     0.0022  0.0196        0.9827
769     0.0025  0.0221        0.9804
770     0.0028  0.0248        0.9779
771     0.0030  0.0279        0.9752
772     0.0033  0.0312        0.9721
773     0.0037  0.0348        0.9688
774     0.0040  0.0388        0.9652
775     0.0044  0.0432        0.9612
776     0.0048  0.0480        0.9568
777     0.0052  0.0531        0.9520
778     0.0056  0.0587        0.9469
779     0.0061  0.0648        0.9413
780     0.0065  0.0713        0.9352
781     0.0070  0.0784        0.9287
782     0.0075  0.0859        0.9216
783     0.0081  0.0939        0.9141
784     0.0086  0.1026        0.9061
785     0.0092  0.1117        0.8974
786     0.0097  0.1215        0.8883
787     0.0103  0.1318        0.8785
788     0.0109  0.1427        0.8682
789     0.0115  0.1542        0.8573
790     0.0121  0.1663        0.8458
791     0.0127  0.1790        0.8337
792     0.0133  0.1923        0.8210
793     0.0139  0.2061        0.8077
794     0.0145  0.2206        0.7939
795     0.0150  0.2356        0.7794
796     0.0156  0.2512        0.7644
797     0.0161  0.2673        0.7488
798     0.0166  0.2839        0.7327
799     0.0171  0.3009        0.7161
800     0.0175  0.3184        0.6991
801     0.0179  0.3364        0.6816
802     0.0183  0.3547        0.6636
803     0.0187  0.3734        0.6453
804     0.0190  0.3923        0.6266
805     0.0192  0.4115        0.6077
806     0.0194  0.4310        0.5885
807     0.0196  0.4506        0.5690
808     0.0197  0.4703        0.5494
809     0.0198  0.4901        0.5297
810     0.0198  0.5099        0.5099
811     0.0198  0.5297        0.4901
812     0.0197  0.5494        0.4703
813     0.0196  0.5690        0.4506
814     0.0194  0.5885        0.4310
815     0.0192  0.6077        0.4115
816     0.0190  0.6266        0.3923
817     0.0187  0.6453        0.3734
818     0.0183  0.6636        0.3547
819     0.0179  0.6816        0.3364
820     0.0175  0.6991        0.3184
821     0.0171  0.7161        0.3009
822     0.0166  0.7327        0.2839
823     0.0161  0.7488        0.2673
824     0.0156  0.7644        0.2512
825     0.0150  0.7794        0.2356
826     0.0145  0.7939        0.2206
827     0.0139  0.8077        0.2061
828     0.0133  0.8210        0.1923
829     0.0127  0.8337        0.1790
830     0.0121  0.8458        0.1663
831     0.0115  0.8573        0.1542
832     0.0109  0.8682        0.1427
833     0.0103  0.8785        0.1318
834     0.0097  0.8883        0.1215
835     0.0092  0.8974        0.1117
836     0.0086  0.9061        0.1026
837     0.0081  0.9141        0.0939
838     0.0075  0.9216        0.0859
839     0.0070  0.9287        0.0784
840     0.0065  0.9352        0.0713
841     0.0061  0.9413        0.0648
842     0.0056  0.9469        0.0587
843     0.0052  0.9520        0.0531
844     0.0048  0.9568        0.0480
845     0.0044  0.9612        0.0432
846     0.0040  0.9652        0.0388
847     0.0037  0.9688        0.0348
848     0.0033  0.9721        0.0312
849     0.0030  0.9752        0.0279
850     0.0028  0.9779        0.0248
851     0.0025  0.9804        0.0221
852     0.0022  0.9827        0.0196
853     0.0020  0.9847        0.0173
854     0.0018  0.9865        0.0153
855     0.0016  0.9881        0.0135
856     0.0015  0.9896        0.0119
857     0.0013  0.9909        0.0104
858     0.0012  0.9920        0.0091
859     0.0010  0.9931        0.0080
860     0.0009  0.9940        0.0069
861     0.0008  0.9948        0.0060
862     0.0007  0.9955        0.0052
863     0.0006  0.9961        0.0045
864     0.0005  0.9966        0.0039
865     0.0005  0.9971        0.0034
866     0.0004  0.9975        0.0029
867     0.0004  0.9979        0.0025
868     0.0003  0.9982        0.0021
869     0.0003  0.9985        0.0018
870     0.0002  0.9987        0.0015



-- 
Dave W. 	(dwallace@dtc.hp.com)
Newsgroups: rec.sport.baseball