Answered

Tanya prepared 4 different letters to be sent to 4 different addresses. For each letter, she prepared an envelope with its correct address. If the 4 letters are to be put into the 4 envelopes at random, what is the probability that only 1 letter will be put into the envelope with its correct address?
A. 1/24
B. 1/8
C. 1/4
D. 1/3
E. 3/8

Answer :

nandhini123

Answer:

The probability that only 1 letter will be put into the envelope with its correct address is [tex]\frac{1}{3}[/tex]

Step-by-step explanation:

Given:

Number of Letters=4

Number of addresses= 4

To Find:

The probability that only 1 letter will be put into the envelope with its correct address=?

Solution:

Let us assume first letter goes in correct envelope and others go in wrong envelopes, then

=> Probability putting the first letter in correct envelope =[tex]\frac{1}{4}[/tex]

=>  Probability putting the second letter in correct envelope =[tex]\frac{2}{3}[/tex]

=>  Probability putting the third letter in correct envelope= [tex]\frac{1}{2}[/tex]

=> Probability putting the fourth letter in correct envelope = 1;  

( only 1 wrong addressed envelope is left);

This event can occur with other 3 envelopes too.

Hence total prob. = [tex]4\times(\frac{1}{4}\times\frac{2}{3}\times\frac{1}{2}\times1)[/tex]

=> [tex]\frac{1}{3}[/tex]

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