All about flooble | fun stuff | Get a free chatterbox | Free JavaScript | Avatars
 perplexus dot info

 Performance Probe (Posted on 2014-10-24)
Four friends Abe, Ben, Cade and Dan sang a quartet. Two of them sang tenor, one sang baritone and one sang bass, not necessarily in that order.

It is also known that:

(i) If Ben was not one of the tenors, then Abe was the baritone.
(ii) If Dan was the baritone, then Cade was the bass.

Determine the probability that:

(a) Ben was a tenor.
(b) Abe was the baritone.

 No Solution Yet Submitted by K Sengupta No Rating

Comments: ( Back to comment list | You must be logged in to post comments.)
 computer solution | Comment 1 of 2
DefDbl A-Z
Dim crlf\$
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

ChDir "C:\Program Files (x86)\DevStudio\VB\projects\flooble"
Text1.Text = ""
crlf\$ = Chr(13) + Chr(10)
Form1.Visible = True
DoEvents
'       tenor,tenor, baritone, bass
perf\$ = "abcd": h\$ = perf\$
Do
good = 1
If InStr(perf\$, "b") > 2 And Mid\$(perf\$, 3, 1) <> "a" Then good = 0
If Mid(perf\$, 3, 1) = "d" And Mid(perf\$, 4, 1) <> "c" Then good = 0
If good Then
ct = ct + 1
Text1.Text = Text1.Text & perf\$ & crlf
If InStr(perf\$, "b") <= 2 Then benten = benten + 1
If Mid(perf\$, 3, 1) = "a" Then abebar = abebar + 1
If Mid(perf\$, 4, 1) = "c" Then cadebass = cadebass + 1
End If
permute perf\$
Loop Until perf\$ = h\$
Text1.Text = Text1.Text & benten & "/" & ct & " =" & mform(benten / ct, " 0.00000000") & crlf
Text1.Text = Text1.Text & abebar & "/" & ct & " =" & mform(abebar / ct, " 0.00000000") & crlf
Text1.Text = Text1.Text & cadebass & "/" & ct & " =" & mform(cadebass / ct, " 0.00000000") & crlf

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

finds the valid filling of the positions as follows (two tenor positions, the baritone position and the bass position in that order):

abcd
abdc
bacd
bdac
bdca
cdab
dbac
dbca
dcab

and the following probabilities:

(a) 10/12 = 0.83333333
(b) 6/12 = 0.50000000
(c) 4/12 = 0.33333333

 Posted by Charlie on 2014-10-24 19:28:50

 Search: Search body:
Forums (0)