Pick 3 Probability

[fenris]

I have a question about pick 3 probabilities. I know that the probability of a particular digit (0-9) of showing up in a particular position is 1/10. I am wondering what the probability of a digit is for just showing up in a draw is? In other words, what is the probability of the number 9 showing up? Is it 3/10?

Thanks...

 

[johnph77]

Not really. There are 1000 different numbers in a Pick 3 draw, ranging from 000 to 999, and therefore 3000 digits. A 9 will appear 300 times in those digits. But when doubles and triples are taken into consideration, a 9 (or any other digit) will only appear 271 times in the 1000 possibilities.

 

[fenris]

Thanks for the help. I had written a small vba macro to confirm the results:

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