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Simpler probability problem? (Posted on 2015-08-11) Difficulty: 1 of 5
An urn contains 5 black and 20 white marbles. They are to be drawn one at a time until all of one color has been exhausted.

What is the probability that the color of the first draw correctly predicts the first color exhausted?

No Solution Yet Submitted by Jer    
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simulation of 100 trials | Comment 10 of 14 |
(In reply to re(4): solution by Charlie)

wwwwwwbwwwbwwwwwwbwwwwbw white exhausted    a match
wwwwwwwwwwwbwwbwbwwbwb black exhausted
bwwbwwwwwwwbwwwwwwwbb black exhausted   a match
wbwwwwwwwwwwbwwwwbwwwwbw white exhausted    a match
wwwwbwwbwwwbwwwwbwwwwb black exhausted
wwwwwbbbbwwb black exhausted
wwwwbbwwwbwwwbwwwwwwb black exhausted
wbwbwwwwwwwbbwwwwwwwb black exhausted
wbwwwwwwbwwwbwwwbwwwb black exhausted
bwwwwwwwwwwwwwwbwwwwbwbw white exhausted
wwwwwwbwbwwwwbwwwwbwwwb black exhausted
bwwwbbwbwwwwwwwwwwb black exhausted   a match
wwbwwwwwwwwbwwwbwwbwb black exhausted
wwwwwbwwwwbwwwwwwwbwwbb black exhausted
wwwbwwwwwwwwwwbwwwbbb black exhausted
bwwbwwwwwwwwwbwwwwwwwww white exhausted
wwwwwbwbwwwwwwwwbwwwbwb black exhausted
wwwwbwwwwwbwbwwwwwwbwb black exhausted
bwbwwwwwwwwwwbwwbwb black exhausted   a match
wwwbwwbwwwwwbbb black exhausted
bwwwwwwbwbwwwwwwwwbwwwww white exhausted
wwbwwwwwwwwwbbwbwwb black exhausted
bwwwwwwwwwwwwwwwwwbwwbw white exhausted
wwwwwbwwwwwbwwwbwwbwwwww white exhausted    a match
wwwwbbwbwwwwwbwb black exhausted
wwwwwwwwwwbbwwwwwwbwwbww white exhausted    a match
wwbwwbwbwwwbb black exhausted
wwwwwwwbwwwwwwwwwwwbwbbw white exhausted    a match
wwbwwwwwwwwwwwwbwwbbwwb black exhausted
bwwwwbwwwwwwwbwwwbwwwwwb black exhausted   a match
wwbwbwwwwwwwbwbwwwb black exhausted
wbwwwwwwwbwwwwwwwwbwwwbb black exhausted
wwwwwbwbwbwwbwwwwwwwb black exhausted
wbwwwwbwwwwwwbwwwwbwwb black exhausted
wwwwwwwbbwwwwwwbbwwwwwww white exhausted    a match
wwbwbwwwwwbwwwwwbwwwwwwb black exhausted
wwwwbwwwwwwbwwwwbwbwwwwb black exhausted
wwwbwwwwwwwbwwbwwwwbwwww white exhausted    a match
wwbwbwwbwwwwbwwb black exhausted
wbbwwwwwwbwwwwbwwwwwb black exhausted
wwwwwwwbbbwwwbb black exhausted
wwwwwwbwwwwwwbwbwwwwbwb black exhausted
wwwbwbwwwwwwbwbwwwwwwwb black exhausted
wwwwwbbbbwwwwwwwwb black exhausted
bwwwwwwwwwbwbwwwwwwwwbww white exhausted
wbbwwwwwwbwwbwwwwwwwwwww white exhausted    a match
wwwwwwbwwwwwwwwwbbwwwbww white exhausted    a match
wwwwbwwwwwwbwbwbwwwwwb black exhausted
wbwwwbwwwwwwwwwwwbwwwbwb black exhausted
bwwwwbwwbwbwwwwwwwwwb black exhausted   a match
wwwbwwwwwwbwwwwbwbwwwwb black exhausted
wwwwwbwwwwwbwwwbwbwwwwwb black exhausted
wwbwbwwwwbwwwwbwwb black exhausted
wwwwwbwwbbwbwwwwwwwwb black exhausted
bwwwwwwwwwwbbbwwwwwwwwwb black exhausted   a match
wwwwwwwwbwwbwwwwbwwbwwwb black exhausted
bwwbwwbwwwwwwwbwwwb black exhausted   a match
bwwwwbwwwwwwwwwbwwbwwwww white exhausted
wbbwwwwwwwwwwwbwbwwwwwb black exhausted
bwwbwbwwwbwwwwwwb black exhausted   a match
wwwwwbwwwwwwbwwwwwbwbwb black exhausted
bwwwwwwbwwwwwwwwwwwwbbwb black exhausted   a match
bbwwwwwwwwwwbwwwwwwwwbww white exhausted
wbwwwbwwwwbwwwbwb black exhausted
wwwwwbwwbwwbwbwwwwwwwb black exhausted
bwwwwwwwwwwbwwwbwbwwwb black exhausted   a match
wwwwwwwwwwbwwwwbbwbwwwwb black exhausted
wbwwwwwbwwwbwwbwb black exhausted
wbwwwwwwbwwwwwwwwwwwwbbb black exhausted
wbwwwwwwwwwwwbwwwbwwbb black exhausted
wwwwbwbwbwwbwwb black exhausted
wwwbwwwwbwwwwwwwwbwwwwbb black exhausted
wwbbwwwwwwwwbwwwwwwbwwwb black exhausted
wwwwwwwwwbbwbwwwwwwwwwbb black exhausted
wwwwbwwwbwwbwwwwwwwwwww white exhausted    a match
wwbwbbwwwwwwwwwwwwwwbwb black exhausted
wwwwwwbbwwwwbwwwwwwwwbb black exhausted
wbbwwwwbwwwwwwwwwwwwwwbw white exhausted    a match
bwwwwwwwwwwwwbwwbwwwwbwb black exhausted   a match
wwbwwwwwwwwwbbwwwwwwbb black exhausted
bwwbwwwwwwwwbwbwb black exhausted   a match
bwwwwwwwwwbwbbwwwwb black exhausted   a match
wwwbwwwwbwwbbb black exhausted
wwbwwwwbwbwwwwwwwwwwwbb black exhausted
wbwbwwwwwwwwwwwwwwwbbwb black exhausted
wwwwbbwwwwwwwwwbwbwwwwww white exhausted    a match
wwwwwwwwwwwbbwbwbwwwwwww white exhausted    a match
wwbwwwwwwwbwwwwwbwwwwww white exhausted    a match
wwwwwwwwwwbwwwwbwwwwwbw white exhausted    a match
wbbwbwbwwwwwwwwwwwwwwwb black exhausted
bwwwwbwbwwwwbwwwwwwwwwww white exhausted
wbwwbwbwwwwwwwwwwwbwwb black exhausted
bwwwbwwwwwwbwwwwwwwbb black exhausted   a match
wwwwwwwbwwwbwbwwbwwwwwb black exhausted
bwwwwwwwwwwwwbwbwwbwwwww white exhausted
bwwbwwbwwwwwwwwwwwbwb black exhausted   a match
wbbwwbwwwwwwwwwwwwwbb black exhausted
wwbbwwwwwbwwwbwwwb black exhausted
bwwwwwwwwwbwwwwwbwwwwwbw white exhausted
wwwwwwbwwwwbwbwwbwwb black exhausted
30 100
 done

In 30 out of 100 trials there's a match between the first color to be exhausted and the first marble drawn. This is more consistent with a 1/3 probability than with a 2/3 probability.

DefDbl A-Z
Dim crlf$


Private Sub Form_Load()
 Form1.Visible = True
 
 Text1.Text = ""
 crlf = Chr$(13) + Chr$(10)

 For trial = 1 To 100
   black = 5: white = 20
   firstOne = 1
   Do
     tot = black + white
     r = Int(Rnd(1) * tot + 1)
     If r <= black Then
       Text1.Text = Text1.Text & "b"
       black = black - 1
       If firstOne Then color1$ = "b": firstOne = 0
     Else
       Text1.Text = Text1.Text & "w"
       white = white - 1
       If firstOne Then color1$ = "w": firstOne = 0
     End If
     If black = 0 Then
       Text1.Text = Text1.Text & " black exhausted"
       If color1 = "b" Then matchct = matchct + 1: Text1.Text = Text1.Text & "   a match"
       Text1.Text = Text1.Text & crlf
       Exit Do
     End If
     If white = 0 Then
       Text1.Text = Text1.Text & " white exhausted"
       If color1 = "w" Then matchct = matchct + 1: Text1.Text = Text1.Text & "    a match"
       Text1.Text = Text1.Text & crlf
       Exit Do
     End If
   Loop
 Next


 Text1.Text = Text1.Text & matchct & Str(trial - 1) & crlf & " done"
  
End Sub


  Posted by Charlie on 2015-08-12 12:27:43
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