Math Is Fun Forum

simone

Member

Registered: 2007-10-05

Posts: 19

probability - help please

I'm having lots of problems with probability questions.
Could you help me solve this? Thank you.

4 different letters are to be sent to 4 different addresses. For each letter there is an envelope with its correct address. If the 4 letters are to be put into the 4 envelopes at random, what it the probability that ony 1 letter will be put into the envelope with its correct address?

thank you

Last edited by simone (2007-10-15 23:24:47)

John E. Franklin

Member

Registered: 2005-08-29

Posts: 3,588

Re: probability - help please

Write out the permutations.
AinA BinB CinC DinD
Let's make four columns labeled inA inB inC and inD envelope.
inA inB inC inD
a    b    c    d
d    c    b    a
c    a    b    d  (d in D, other 3 wrong envelope)
d    b    a    c  (b in B)
b    d    a    c
c    a    d    b
a    d    b    c (a in A)
c    b    d    a (b in B)
b    a    c    d (c and d right, so ignore)
d    c    a    b
b    d    c    a (c in C)
a    c    d    b (a in A)
d    a    b    c
c    b    a    d (ignore 2 right)
b    c    d    a
a    d    c    b (ignore 2 right)
c    d    a    b
b    a    d    c
a    b    d    c (ignore 2 right)
c    d    b    a
a    c    b    d (ignore 2 right a & d)
d    b    c    a (ignore 2 right b & c)
d    a    c    b (c in C)
b    c    a    d (d in D)

8 out of 24 are only 1 right & 3 wrong.
6 out of 24 are 2 right & 2 wrong.
9 out of 24 are none right & 4 wrong.
1 out of 24 is all 4 right & none wrong!!
8 + 6 + 9 + 1 = 24
4 x 3 x 2 = 24

Last edited by John E. Franklin (2007-10-16 03:42:19)

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