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Probability Question

Topic closed. 18 replies. Last post 12 years ago by johnph77.

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Posted: March 28, 2005, 10:32 am - IP Logged

In a pick 3 lottery, each digit (0-9) has a probability of 1/10 of showing up in a particular position. I would like to know what the probability is for a number to show up? Is it 3/10?

    RJOh's avatar - chipmunk
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    Posted: March 28, 2005, 11:06 am - IP Logged

    Of the 1000 possible combinations in a pick3 lottery there are three digits.  A number can appear 100 times in the first digit,10 times in second digit and 10 times in the third digit, that would be 120/1000.

    RJOh 

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      Posted: March 28, 2005, 11:17 am - IP Logged

      RJOh, Thank you very much for the response! It got me to start thinking about the probabilites in a new light, with a new understanding. Thanks...

        RJOh's avatar - chipmunk
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        Posted: March 28, 2005, 11:39 am - IP Logged

        Correction.

        Quote: Originally posted by RJOh on March 28, 2005







        Of the 1000 possible combinations in a pick3 lottery there are three digits.  A number can appear 100 times in the first digit,100 times in second digit and 100 times in the third digit, that would be 300/1000.

        RJOh 







        You were right the first time.

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          Posted: March 28, 2005, 1:05 pm - IP Logged

          I wrote up this little macro for excel to actually count how many occurances of a particular digit are within the range 000 to 999. The macro tells me that there are 271 numbers that can contain a particular digit. So that would make the probability 271/1000 = 27.1% slightly less then 30%.



          [code]

          Public Sub countNumbers()

          Dim counts(9) As Long

          Dim numberCounter As Long

          Dim number As String

          Dim numberToTest As Long



          Const upperLimit As Long = 999

          For numberCounter = 0 To upperLimit

              number = Format(numberCounter, "00#")

              For numberToTest = 0 To 9 'loop through the digits and see if any of them are in the draw number

                  If InStr(1, number, numberToTest) > 0 Then

                     counts(numberToTest) = counts(numberToTest) + 1

                  End If

              Next

          Next



          MsgBox "0 = " & counts(0) & vbNewLine & _

                 "1 = " & counts(1) & vbNewLine & _

                 "2 = " & counts(2) & vbNewLine & _

                 "3 = " & counts(3) & vbNewLine & _

                 "4 = " & counts(4) & vbNewLine & _

                 "5 = " & counts(5) & vbNewLine & _

                 "6 = " & counts(6) & vbNewLine & _

                 "7 = " & counts(7) & vbNewLine & _

                 "8 = " & counts(8) & vbNewLine & _

                 "9 = " & counts(9) & vbNewLine



          End Sub

          [/code]

            RJOh's avatar - chipmunk
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            Posted: March 28, 2005, 6:01 pm - IP Logged

            10 D=0:CLS:INPUT "NUMBER TO COUNT AND PRINT (0-9) ",N
            20 IF N>9 THEN 10
            30 FOR A=0 TO 9
            40 FOR B=0 TO 9
            50 FOR C=0 TO 9
            60 C$= CHR$(A+48)+CHR$(B+48)+CHR$(C+48)
            70 IF A=N OR B=N OR C=N THEN D=D+1:PRINT D;". ";C$
            80 NEXT C
            90 NEXT B
            100 NEXT A

            I wrote the above basic program that counts and prints out every combinations that include the number N and it counts 271 also. 

            RJOh

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              johnph77's avatar - avatar
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              Posted: March 28, 2005, 6:11 pm - IP Logged

              Fenris and RJOh are correct - 271. A 9 will appear 300 times in the 3000 digits present in the 1000 possibilities in a Pick 3 draw but due to doubles and the triple will appear only 271 times in all 3-digit possibilities

              gl

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                RJOh's avatar - chipmunk
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                Posted: March 28, 2005, 7:53 pm - IP Logged

                That makes sense. The number 9 appears 300 times in 271 combinations.

                    009    019    029    039    049    059    069    079    089    090
                    091    092    093    094    095    096    097    098    099    109
                    119    129    139    149    159    169    179    189    190    191
                    192    193    194    195    196    197    198    199    209    219
                    229    239    249    259    269    279    289    290    291    292
                    293    294    295    296    297    298    299    309    319    329
                    339    349    359    369    379    389    390    391    392    393
                    394    395    396    397    398    399    409    419    429    439
                    449    459    469    479    489    490    491    492    493    494
                    495    496    497    498    499    509    519    529    539    549
                    559    569    579    589    590    591    592    593    594    595
                    596    597    598    599    609    619    629    639    649    659
                    669    679    689    690    691    692    693    694    695    696
                    697    698    699    709    719    729    739    749    759    769
                    779    789    790    791    792    793    794    795    796    797
                    798    799    809    819    829    839    849    859    869    879
                    889    890    891    892    893    894    895    896    897    898
                    899    900    901    902    903    904    905    906    907    908
                    909    910    911    912    913    914    915    916    917    918
                    919    920    921    922    923    924    925    926    927    928
                    929    930    931    932    933    934    935    936    937    938
                    939    940    941    942    943    944    945    946    947    948
                    949    950    951    952    953    954    955    956    957    958
                    959    960    961    962    963    964    965    966    967    968
                    969    970    971    972    973    974    975    976    977    978
                    979    980    981    982    983    984    985    986    987    988
                    989    990    991    992    993    994    995    996    997    998
                    999

                RJOh

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                  Posted: March 29, 2005, 11:46 am - IP Logged

                  Thanks guys I really appreciate the help. RJoh, thanks for the confirmation from a different language!

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                    Posted: March 31, 2005, 11:21 am - IP Logged

                    Or, in probability terms,



                    P(a 9 somewhere) = 1- P(no nines) = 1 - (P(first not 9)*P(second not 9)*P(third not 9)) = 1 - .9*.9*.9 = 1 - .729 = .271

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                      Posted: March 31, 2005, 12:09 pm - IP Logged
                      Quote: Originally posted by Bingo Long on March 31, 2005

                      Or, in probability terms,



                      P(a 9 somewhere) = 1- P(no nines) = 1 - (P(first not 9)*P(second not 9)*P(third not 9)) = 1 - .9*.9*.9 = 1 - .729 = .271






                      Ahh, that makes sense. I was trying to directly calculate the probability.



                      So, then what would the probability of at least 2 digits (say 9) appearing in a particular drawing be?



                      p(2 nines) = P(a 9 somewhere)*P(a 9 somewhere) =0.271*0.271 = 0.073441



                      Also are there any good books or references out there on this type of probability work?
                        LANTERN's avatar - kilroy 28_173_reasonably_small.jpg
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                        Posted: March 31, 2005, 12:38 pm - IP Logged
                        Quote: Originally posted by RJOh on March 28, 2005



                        That makes sense. The number 9 appears 300 times in 271 combinations.

                            009    019    029    039    049    059    069    079    089    090
                            091    092    093    094    095    096    097    098    099    109
                            119    129    139    149    159    169    179    189    190    191
                            192    193    194    195    196    197    198    199    209    219
                            229    239    249    259    269    279    289    290    291    292
                            293    294    295    296    297    298    299    309    319    329
                            339    349    359    369    379    389    390    391    392    393
                            394    395    396    397    398    399    409    419    429    439
                            449    459    469    479    489    490    491    492    493    494
                            495    496    497    498    499    509    519    529    539    549
                            559    569    579    589    590    591    592    593    594    595
                            596    597    598    599    609    619    629    639    649    659
                            669    679    689    690    691    692    693    694    695    696
                            697    698    699    709    719    729    739    749    759    769
                            779    789    790    791    792    793    794    795    796    797
                            798    799    809    819    829    839    849    859    869    879
                            889    890    891    892    893    894    895    896    897    898
                            899    900    901    902    903    904    905    906    907    908
                            909    910    911    912    913    914    915    916    917    918
                            919    920    921    922    923    924    925    926    927    928
                            929    930    931    932    933    934    935    936    937    938
                            939    940    941    942    943    944    945    946    947    948
                            949    950    951    952    953    954    955    956    957    958
                            959    960    961    962    963    964    965    966    967    968
                            969    970    971    972    973    974    975    976    977    978
                            979    980    981    982    983    984    985    986    987    988
                            989    990    991    992    993    994    995    996    997    998
                            999

                        RJOh

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                          RJOh's avatar - chipmunk
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                          Posted: March 31, 2005, 1:34 pm - IP Logged

                          Quote: Originally posted by LANTERN on March 31, 2005







                          This means that if you now for sure that the number 9 will be coming out next on any one of the 3 pick 3 positions and you can to play it straight including doubles and triples then you need to buy 271 straight pick 3 combos to win straight........ 








                          For pick3 games, Maybells Quikwheel (a wheel program from the old Maybell website) wheels 271 lines for a straight hit if key number hits and only 54 lines for a box hit if the key number hits.

                          RJOh 

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                            Posted: March 31, 2005, 3:17 pm - IP Logged

                            I was thinking more along the lines of this:



                            If nine hit in the last three draws, what are the odds that it will hit in the next draw. In other words, what is the probability that 9 will hit 4 times in a row?



                            That would be, .271^4 =0.00539 or 0.539% or 1/185.4



                            So it is a good chance that 9 won't show up in the next draw. Now if you kept track of all of these digits and did a similar thing, then you may have a good way of reducing the number of potentials. Keep in mind a similar thing can be done with consecutive misses.



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                              Posted: March 31, 2005, 3:33 pm - IP Logged

                              because of all the undue manipulations by the state lotteries such as predraws and whatever else, fact(s) and expected mathematical probabilities might not corelate too well, you would be surprised as to what is possible when a lot of money is at stake and they have the ability to manipulate the numbers and results in almost anyway that they want to.

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