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 Colored Candy Choice (Posted on 2016-05-25)
I have 6 pieces of candy: two each of 3 different colors. They taste especially good if eaten two at a time, provided the colors are different.

These candies are in an opaque bag from which I pick two at a time. If they are different colors I eat them together (yum) but if they are the same I put them back in and draw again. I will repeat this process to eat two more.

What is the probability the last two candies will be of differing colors?

Repeat with two each of 4 colors.
Repeat with two each of 5 colors.

 No Solution Yet Submitted by Jer No Rating

Comments: ( Back to comment list | You must be logged in to post comments.)
 re: Second part | Comment 7 of 10 |
(In reply to Second part by armando)

A simulation

DefDbl A-Z
Dim crlf\$

Form1.Visible = True

Text1.Text = ""
crlf = Chr\$(13) + Chr\$(10)

For tr = 1 To 100000
clr\$ = "aabbccdd"
Do
r1 = Int(Len(clr) * Rnd(1) + 1)
r2 = Int(Len(clr) * Rnd(1) + 1)
If Mid(clr, r1, 1) <> Mid(clr, r2, 1) Then
If r1 > r2 Then h = r1: r1 = r2: r2 = h
clr = Left(clr, r1 - 1) + Mid(clr, r1 + 1, r2 - r1 - 1) + Mid(clr, r2 + 1)
End If
Loop Until Len(clr) = 2
If Left(clr, 1) <> Right(clr, 1) Then hitct = hitct + 1
Next
Text1.Text = Text1.Text & hitct / 100000

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

End Sub

comes up with

.87736

for part 2

and a variant produces

0.88996

for part 3

throwing in a randomize timer shows these results for part 2:

0.87865
0.87578
0.87658

on successive runs.

and for part 3,

0.89272
0.89239
0.89133

 Posted by Charlie on 2016-05-25 21:05:17

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