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# my uncle wrote three different letters and addressed three envelopes. then he went outside for a walk. while he was out, his little daughter

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my uncle wrote three different letters and addressed three envelopes. then he went outside for a walk. while he was out, his little daughter put a letter into each envelope and sealed it. what is the probability that none of the letters was in the correct envelope?

Guest Jan 16, 2015

#7
+20681
+13

Hi Rosala,

here all possibilities:

I.

Letter 1 put into envelope 1

Letter 2 put into envelope 2              or          Letter 2 put into envelope 3

Letter 3 must be in envelope 3                       Letter 3 must be in envelope 2

we have:

1. Letter 1 in envelope 1

Letter 2 in envelope 2

Letter 3 in envelope 3

2. Letter 1 in envelope 1

Letter 2 in envelope 3

Letter 3 in envelope 2

we can change places 3 times. Letter 1 can start in envelope 1 or in envelope 2 or in envelope 3

so we have 2 * 3 = 6

heureka  Jan 16, 2015
#1
+20681
+8

my uncle wrote three different letters and addressed three envelopes. then he went outside for a walk. while he was out, his little daughter put a letter into each envelope and sealed it. what is the probability that none of the letters was in the correct envelope?

$$\small{\text{ {okay} \text{ {false} \begin{array}{|l|c|c|c|} \hline n& letter 1 & letter 2 & letter 3  \\ \hline 1& envelope\ {1} & envelope\ {2} & envelope\ {3}  \\ 2& envelope\ {1} & envelope\ {3} & envelope\ {2}  \\ 3& envelope\ {2} & envelope\ {1} & envelope\ {3}  \\ {4}& envelope\ {2} & envelope\ {3} & envelope\ {1}  \\ {5}& envelope\ {3} & envelope\ {1} & envelope\ {2}  \\ 6& envelope\ {3} & envelope\ {2} & envelope\ {1}  \\ \hline \end{array} }}$$

The probability that none of the letters was in the correct envelope is  $$\frac{2}{6} = \frac{1}{3} = 33.\overline{3}\ \%$$

heureka  Jan 16, 2015
#2
+11852
+13

rosala  Jan 16, 2015
#3
+20681
+13

Hi Rosala,

There are 6 different possibilities to put 3 letters into 3 envelopes. I have numbered serially them with from 1 to 6. Then I have looked which letters agree with which envelopes. There remain 2 possibilities in those all 3 letters in the envelopes are wrong franked. Then the probability is: 2/6

heureka  Jan 16, 2015
#4
+11852
+13

how come 6, it said ' what is the probability that none of the letters was in the correct envelope'  , there are 3 letters and 3 envelopes so it should be 9.......im sooo confused Heureka!

rosala  Jan 16, 2015
#5
+20681
+13

Hi Rosala,

for example if Letter 1 is in envelope 1 then you can't put Letter 2 or Letter 3 into envelope 1.

heureka  Jan 16, 2015
#6
+11852
+13

hi heaureka,...so now i understood why not 9 ...but would you mind telling me why6?im just so confused thats why!thanks!

rosala  Jan 16, 2015
#7
+20681
+13

Hi Rosala,

here all possibilities:

I.

Letter 1 put into envelope 1

Letter 2 put into envelope 2              or          Letter 2 put into envelope 3

Letter 3 must be in envelope 3                       Letter 3 must be in envelope 2

we have:

1. Letter 1 in envelope 1

Letter 2 in envelope 2

Letter 3 in envelope 3

2. Letter 1 in envelope 1

Letter 2 in envelope 3

Letter 3 in envelope 2

we can change places 3 times. Letter 1 can start in envelope 1 or in envelope 2 or in envelope 3

so we have 2 * 3 = 6

heureka  Jan 16, 2015
#8
+94140
+8

Thanks Heureka

And thanks for the good questions Rosala.

Melody  Jan 16, 2015
#9
+11852
+8

Thanks Melody and Heureka!

Thank you Heureka for all the hard work for me!i really appreciate it!thanks!

rosala  Jan 16, 2015