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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

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

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.

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 = 1/2Sub DiceGameTest()RandomizeDim NewValue1 As SingleDim NewValue2 As SingleDim LastValue1 As SingleDim LastValue2 As SingleDim StudentAwin As SingleDim StudentBwin As SingleDim Winner As SingleFor 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 = 0Next itotal = StudentBwin + StudentAwinSelection.TypeText Text:=str(StudentAwin / total)End Sub