Which day of the week (Sunday, Monday, etc.) is the probability largest to fall on the 13th of a random month, in a random year?

Or is this probability the same for each day of the week?

I wrote a Visual Basic program that counts beginning with 2004. I used the correct definition of a leap year: a non-century year divisible by 4, or a century divisible by 400. I verified program results for 2004-2005. 

For 2004-1000000, Friday is most likely -- Friday the 13th. There will be 1714060 Sundays, 1709071 Mondays, 1709070 Tuesdays, 1714060 Wednesdays, 1706574 Thursdays, 1716555 Fridays and 1706574 Saturdays that fall on the 13th of the month. (Of course, by 1000000 AD, only Alan Greenspan will still be around to verify this).

Imports System
Imports System.IO
Imports System.Text
Imports System.Runtime.InteropServices
Imports System.Math
Module Module1
    Sub Main()
        Randomize()
        Dim strgo As String
        strgo = "y"
        While strgo = "y"
            mainline()
            Console.WriteLine("Again ? (y/n)")
            strgo = LCase(Console.ReadLine())
        End While
    End Sub
    Sub mainline()
        Dim inttargetyear As Integer
        Dim intdays(7, 1) As Integer
        Dim intsub As Integer
        Dim intweekday As Integer = 0
        Dim intweekday2 As Integer
        Dim intweekday7 As Integer
        Dim intmonth As Integer
        Dim strday As String
        Dim strleapyear As String
        Dim strlastyear As String
        inttargetyear = 0
        While inttargetyear < 2004
            Console.WriteLine("Enter ending year (>= 2004)")
            inttargetyear = Int(Console.ReadLine())
        End While
        For index1 As Integer = 0 To 6
            intdays(index1, 0) = 0
        Next
        intweekday = 0
        For index0 As Integer = 2004 To inttargetyear
            If index0 Mod 400 = 0 Then
                strleapyear = "y"
            ElseIf index0 Mod 100 = 0 And _
            index0 Mod 400 <> 0 Then
                strleapyear = "n"
            ElseIf index0 Mod 4 = 0 Then
                strleapyear = "y"
            Else
                strleapyear = "n"
            End If
            If index0 > 2004 Then
                If (index0 - 1) Mod 400 = 0 Then
                    strlastyear = "y"
                ElseIf (index0 - 1) Mod 100 = 0 And _
                (index0 - 1) Mod 400 <> 0 Then
                    strlastyear = "n"
                ElseIf (index0 - 1) Mod 4 = 0 Then
                    strlastyear = "y"
                Else
                    strlastyear = "n"
                End If
            End If
            If index0 = 2004 Then
                intweekday7 = 4
            ElseIf strlastyear = "y" Then
                intweekday7 += 2
            Else
                intweekday7 += 1
            End If
            intweekday7 = intweekday7 Mod 7
            intweekday = 0
            intweekday2 = intweekday7 - 1
            intmonth = 1
            If strleapyear = "n" Then
                For index1 As Integer = 1 To 365
                    intweekday += 1
                    intweekday2 += 1
                    If intweekday = 29 Then
                        If intmonth = 2 Then
                            intmonth += 1
                            intweekday = 1
                        End If
                    ElseIf intweekday = 31 Then
                        If intmonth = 4 Or intmonth = 6 _
                        Or intmonth = 9 Or _
                        intmonth = 11 Then
                            intmonth += 1
                            intweekday = 1
                        End If
                    ElseIf intweekday = 32 Then
                        If intmonth <> 2 And intmonth <> 4 And _
                        intmonth <> 6 And intmonth <> 9 And intmonth <> 11 Then
                            intmonth += 1
                            intweekday = 1
                        End If
                    End If
                    If intweekday = 13 Then
                        intdays(intweekday2 Mod 7, 0) += 1
                    End If
                Next
            Else
                For index1 As Integer = 1 To 366
                    intweekday += 1
                    intweekday2 += 1
                    If intweekday = 30 Then
                        If intmonth = 2 Then
                            intmonth += 1
                            intweekday = 1
                        End If
                    ElseIf intweekday = 31 Then
                        If intmonth = 4 Or intmonth = 6 _
                        Or intmonth = 9 Or _
                        intmonth = 11 Then
                            intmonth += 1
                            intweekday = 1
                        End If
                    ElseIf intweekday = 32 Then
                        If intmonth <> 2 And intmonth <> 4 And _
                        intmonth <> 6 And intmonth <> 9 And intmonth <> 11 Then
                            intmonth += 1
                            intweekday = 1
                        End If
                    End If
                    If intweekday = 13 Then
                        intdays(intweekday2 Mod 7, 0) += 1
                    End If
                Next
            End If
        Next
        For index1 As Integer = 0 To 6
            getday(index1, strday)
            Console.WriteLine(strday & ": " & _
            Str(intdays(index1, 0)))
        Next
    End Sub
    Sub getday(ByRef index1, ByRef strday)
        Select Case index1
            Case 0
                strday = "Sunday"
            Case 1
                strday = "Monday"
            Case 2
                strday = "Tuesday"
            Case 3
                strday = "Wednesday"
            Case 4
                strday = "Thursday"
            Case 5
                strday = "Friday"
            Case 6
                strday = "Saturday"
        End Select
    End Sub
End Module

 

Edited on August 13, 2004, 2:08 pm

Posted by Penny on 2004-08-13 13:17:38