Six balls are at the front of the classroom, and six students are each assigned a different colored ball.
Then they are asked to go up one at a time and take the ball they were assigned.
However, the first student doesn't like the color he was assigned, so he picks randomly from the remaining five.
After that, each successive student takes the color they were assigned if it's available, otherwise they choose randomly from the remaining balls.
What is the probability that the last student gets the ball they were assigned?
DefDbl A-Z
Dim crlf$, remain$, chosen$, ct, denom, prob, tt
Private Sub Form_Load()
Text1.Text = ""
crlf$ = Chr(13) + Chr(10)
Form1.Visible = True
DoEvents
remain$ = "ABCDEF": denom = 1
addon
Text1.Text = Text1.Text & crlf & ct & " " & ct / prob & " " & prob & crlf
Text1.Text = Text1.Text & tt
End Sub
Sub addon()
DoEvents
If chosen = "" Then st = 2 Else st = 1
fin = Len(remain)
If chosen > "" Then
srch$ = Mid("BCDEF", Len(chosen), 1)
ix = InStr(remain, srch)
If ix > 0 Then st = ix: fin = ix
End If
For psn = st To fin
chosen = chosen + Mid(remain, psn, 1)
denom = denom * (fin - st + 1)
remain = Left(remain, psn - 1) + Mid(remain, psn + 1)
If Len(chosen) = 6 Then
If Right(chosen, 1) = "F" Then ct = ct + denom: prob = prob + 1 / denom
Text1.Text = Text1.Text & chosen & " " & ct & " " & mform(1 / denom, "0.00000000") & crlf
tt = tt + 1 / denom
Else
addon
End If
remain = Left(remain, psn - 1) + Right(chosen, 1) + Mid(remain, psn)
chosen = Left(chosen, Len(chosen) - 1)
denom = denom / (fin - st + 1)
Next
End Sub
Function mform$(x, t$)
a$ = Format$(x, t$)
If Len(a$) < Len(t$) Then a$ = Space$(Len(t$) - Len(a$)) & a$
mform$ = a$
End Function
finds
BACDEF 25 0.04000000
BCADEF 125 0.01000000
BCDAEF 425 0.00333333
BCDEAF 1025 0.00166667
BCDEFA 1025 0.00166667
BCDFEA 1025 0.00333333
BCEDAF 1225 0.00500000
BCEDFA 1225 0.00500000
BCFDEA 1225 0.01000000
BDCAEF 1300 0.01333333
BDCEAF 1450 0.00666667
BDCEFA 1450 0.00666667
BDCFEA 1450 0.01333333
BECDAF 1500 0.02000000
BECDFA 1500 0.02000000
BFCDEA 1500 0.04000000
CBADEF 1520 0.05000000
CBDAEF 1580 0.01666667
CBDEAF 1700 0.00833333
CBDEFA 1700 0.00833333
CBDFEA 1700 0.01666667
CBEDAF 1740 0.02500000
CBEDFA 1740 0.02500000
CBFDEA 1740 0.05000000
DBCAEF 1755 0.06666667
DBCEAF 1785 0.03333333
DBCEFA 1785 0.03333333
DBCFEA 1785 0.06666667
EBCDAF 1795 0.10000000
EBCDFA 1795 0.10000000
FBCDEA 1795 0.20000000
1795 4487.5 0.4
1
0.4 is the probability asked for.
The 1 at the end verifies the probabilities add to 1.
A simulation verifies the 0.4 probablity:
DefDbl A-Z
Dim crlf$, ct, trials
Private Sub Form_Load()
Text1.Text = ""
crlf$ = Chr(13) + Chr(10)
Form1.Visible = True
DoEvents
sup0$ = "ABCDEF"
Randomize Timer
For tr = 1 To 100000
supply$ = sup0: used$ = ""
For player = 1 To 6
If player = 1 Then r = Int(Rnd(1) * 5 + 2) Else r = Int(Rnd(1) * Len(supply) + 1)
ix = InStr(supply, Mid(sup0, player, 1))
If player > 1 And ix > 0 Then r = ix
used = used + Mid(supply, r, 1)
supply = Left(supply, r - 1) + Mid(supply, r + 1)
Next
If Right(used, 1) = "F" Then ct = ct + 1
trials = trials + 1
DoEvents
Next
Text1.Text = Text1.Text & ct & Str(trials) & Str(ct / trials) & crlf
End Sub
succ. trials prob.
39949 100000 .39949
Edited on April 25, 2019, 3:28 pm
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Posted by Charlie
on 2019-04-24 16:44:02 |
computer assissted solution
