[Badminton]

Use This Code at microsoft word 2010 macro VBA to test this problem.

Sub BadmintonTest()
Dim JohnWin As Single
Dim JulieWin As Single
Dim P5of9 As Single
Dim P4of7 As Single
    Randomize
    For i = 1 To 500000
        For j = 1 To 9
            NewValue = Int((2 * Rnd) + 1)
            If NewValue = 1 Then JohnWin = JohnWin + 1
            If NewValue = 2 Then JulieWin = JulieWin + 1
            If JulieWin = 5 Then P5of9 = P5of9 + 1
        Next j
        JulieWin = 0
    Next i
    Selection.TypeText Text:=" percentage 5of9 = " + str(P5of9 / 5000000)

    For i = 1 To 500000
        For j = 1 To 7
            NewValue = Int((2 * Rnd) + 1)
            If NewValue = 1 Then JohnWin = JohnWin + 1
            If NewValue = 2 Then JulieWin = JulieWin + 1
            If JulieWin = 4 Then P4of7 = P4of7 + 1
        Next j
        JulieWin = 0
    Next i
    Selection.TypeText Text:="     percentage 4of7 = " + str(P4of7 /I run th 5000000)
End Sub

----------------------

I run the code above and find this result

percentage 5of9 =  .0754452      percentage 4of7 =  .0727584
percentage 5of9 =  .0753496      percentage 4of7 =  .072915 
percentage 5of9 =  .0752444      percentage 4of7 =  .0727264 
percentage 5of9 =  .0751622      percentage 4of7 =  .0725046

So it more likely that julie will win 5 out of 9 games than 4 out of 7

[Dice Game]

3 times running the simulation, and I get this result :

 0.4985224
 0.4985202
 0.4985316

Even it seems student B winning chance is a bit bigger than student A

 

[Dice Game]

If anyone understand a bit VBA programming, please check my code, wheather there are some mistake there.

What I do at the simulation is generating random number (1 to 6) twice in each turn, 
Let say dice1 = value1 and dice 2 = value2 than

if value1 = 6 and value2 = 6 then Student A win  (6+6 = 12)
if value1 + value2 = 7 and lastValue1 + lastValue2 = 7 then student B win
if no winner, I repeat until the winner found.

After the winner found, I repeat all the game again 5 million times
After 5 million times I compare student A winning times with student B winning times,
And I find both student have equal chance to win

It take about 10 to 15 second for my computer to do this simulation.

[Dice Game]

Use This simulaton on your microsoft office macro and you will get p = 1/2 as the answer

Use This code in your microsoft office 2010 and you will get p = 1/2

Sub DiceGameTest()
Randomize
Dim NewValue1 As Single
Dim NewValue2 As Single
Dim LastValue1 As Single
Dim LastValue2 As Single
Dim StudentAwin As Single
Dim StudentBwin As Single
Dim Winner As Single

For i = 1 To 5000000
   LastValue1 = 0
   LastValue2 = 0
   Winner = 0
   While Winner = 0
      LastValue1 = NewValue1
      LastValue2 = NewValue2
      NewValue1 = Int((6 * Rnd) + 1)
      NewValue2 = Int((6 * Rnd) + 1)
      If NewValue1 = 6 And NewValue2 = 6 Then Winner = 1
      If NewValue1 + NewValue2 = 7 And LastValue1 + LastValue2 = 7 Then Winner = 2
   Wend
   If Winner = 1 Then StudentAwin = StudentAwin + 1
   If Winner = 2 Then StudentBwin = StudentBwin + 1
   Winner = 0
Next i
total = StudentBwin + StudentAwin
Selection.TypeText Text:=str(StudentAwin / total)
End Sub