[net.math] A Different Simple Statistics Problem

aark@ihuxe.UUCP (08/25/83)

Now that we've beaten the three-cabinets-gold-and-silver-coins problem
to death, here's another simple problem in the same vein:

I have just written four letters to four different people and have
addressed the four envelopes.  In a fit of laziness I decide to stuff
the letters into the envelopes at random, rather than stuffing each
letter into the correct envelope.

What is the probability that exactly three of the letters get into the
right envelopes?
-- 
	Alan R. Kaminsky
	Bell Laboratories, Naperville, IL
	...ihnp4!ihuxe!aark

halle1@houxz.UUCP (08/25/83)

After much thought and pages and pages of calculations, I have the answer.
Gurervfnmrebpunapr.  Vsguerrgurasbhe.
(Rot 13, spacing surpressed.)

fremont@hplabs.UUCP (Michael J. Fremont) (08/26/83)

The probability of getting EXACTLY three correct envelopes is ZERO,
because if you got three right, there is only one envelope to put
the last letter in, and that is ALSO the right envelope -> you got 4
right.
mike

allan@qusavx.UUCP (08/26/83)

Must be 2/3  :-)

israel@umcp-cs.UUCP (08/28/83)

From someone:

	I have just written four letters to four different people and
	have addressed the four envelopes.  In a fit of laziness I
	decide to stuff the letters into the envelopes at random,
	rather than stuffing each letter into the correct envelope.

	What is the probability that exactly three of the letters get
	into the right envelopes?

	---------

From someone else:

	The answer is zero.

	---------

Well, things work differently in the drug business.  I happen to supply
three people, Ronald Reagan, Margaret Thatcher, and George Smith (a
drug addict customer of mine, who currently goes to Podunk State
University).  I also am sending a letter to George Smith (my old
teacher at Podunk State U.) telling him to change my 'F' to an 'A'
or I'll burn his wife down.

I prepare the drugs, paste together newspaper headlines for the other
letter and then address four envelopes as follows:

1) 1600 Pennsylvania Ave. (The White House; Ronnie).
2) 10 Downing Street (My old chum Maggie).
3) 27 Kalamazoo Court (My old HS buddie George, his home address).
4) Podunk State University (my old professor; he never gives out
   his home address).

I put Ronnie's package and Maggie's package into the proper envelopes but
I switch the two Georges' packages.  Podunk State U.'s mail service
always prides itself on efficiency and on always delivering packages to
the proper address, so they opened and examined the package.  Realizing
that it was intended for George Smith the Drug Addict, rather than
George Smith the Professor, they delivered it to the proper address.

Now, three out of the four package got to the proper location
sucessfully, and the fourth got to the wrong address (George Smith, the
Druggie).  (BTW, luckily the drugs got to George right after the
threatening letter did because the letter scared him so bad that he
really needed the stuff!!)

Now, given this additional information, who can tell what the
probability of this happening is?
-- 

~~~ Bruce
Computer Science Dept., University of Maryland
{rlgvax,seismo}!umcp-cs!israel (Usenet)    israel.umcp-cs@Udel-Relay (Arpanet)