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 Playing With Marbles II (Posted on 2014-08-29)
Contents of three identical looking bags are as follows:

Bag 1: Five black marbles, three red marbles and one white marble.
Bag 2: Five red marbles, three white marbles and one black marble.
Bag 3: Five white marbles, three black marbles and one red marble.

You choose one of the three identical looking bags at random.
After choosing a bag you draw two marbles out at random. You notice that the first one is black, and the second one is white.

You then put the two marbles back in the bag they came from and draw two marbles out of the same bag at random.

What is the probability that the first marble drawn is black and the second marble drawn is white?

 No Solution Yet Submitted by K Sengupta No Rating

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 simulation verification Comment 2 of 2 |
(In reply to solution by Charlie)

DefDbl A-Z
Dim crlf\$, c\$(2)

ChDir "C:\Program Files (x86)\DevStudio\VB\projects\flooble"
Text1.Text = ""
crlf\$ = Chr(13) + Chr(10)
Form1.Visible = True
DoEvents

Randomize Timer
For trial = 1 To 16560
Do
bag = Int(3 * Rnd(1) + 1)
m = 0
For chce = 1 To 2
Do
marble = Int(9 * Rnd(1) + 1)
Loop Until marble <> m
m = marble
Select Case bag
Case 1
Select Case marble
Case Is <= 5
c\$(chce) = "b"
Case 6 To 8
c\$(chce) = "r"
Case Else
c\$(chce) = "w"
End Select

Case 2
Select Case marble
Case Is <= 5
c\$(chce) = "r"
Case 6 To 8
c\$(chce) = "w"
Case Else
c\$(chce) = "b"
End Select

Case 3
Select Case marble
Case Is <= 5
c\$(chce) = "w"
Case 6 To 8
c\$(chce) = "b"
Case Else
c\$(chce) = "r"
End Select
End Select
Next chce
Loop Until c\$(1) = "b" And c\$(2) = "w"
m = 0
For chce = 1 To 2
Do
marble = Int(9 * Rnd(1) + 1)
Loop Until marble <> m
m = marble
Select Case bag
Case 1
Select Case marble
Case Is <= 5
c\$(chce) = "b"
Case 6 To 8
c\$(chce) = "r"
Case Else
c\$(chce) = "w"
End Select

Case 2
Select Case marble
Case Is <= 5
c\$(chce) = "r"
Case 6 To 8
c\$(chce) = "w"
Case Else
c\$(chce) = "b"
End Select

Case 3
Select Case marble
Case Is <= 5
c\$(chce) = "w"
Case 6 To 8
c\$(chce) = "b"
Case Else
c\$(chce) = "r"
End Select
End Select
Next chce
If c\$(1) = "b" And c\$(2) = "w" Then hits = hits + 1
If trial Mod 1656 = 0 Then
Text1.Text = Text1.Text & Str(hits) & Str(trial) & Str(hits / trial) & crlf
End If
Next

Text1.Text = Text1.Text & crlf & " done"
End Sub

One run finds 2599 out of 16560 trials; the next, 2554 out of 16560.

 Posted by Charlie on 2014-08-29 12:16:17

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