Ask Questions, Get Answers

Want to ask us a question? Click here
Browse Questions
Home  >>  CBSE XI  >>  Math  >>  Probability
0 votes

Three letters are dictated to three persons and an envelope is addressed to each of them,the letters are inserted into the envelopes at random so that each envelope contains exactly one letter.Find the probability that at least one letter is in its proper envelope.

$\begin{array}{1 1}(A)\;\large\frac{2}{3}\\(B)\;\large\frac{5}{3}\\(C)\;\large\frac{7}{3}\\(D)\;\text{None of these}\end{array} $

Can you answer this question?

1 Answer

0 votes
  • Required probability =$\large\frac{\text{Number of favorable outcomes}}{\text{Total number of outcomes}}=\frac{n(E)}{n(S)}$
Step 1:
Let the envelope be denoted by $E_1,E_2,E_3$ and the corresponding letters by $L_1,L_2,L_3$
Atleast one letter should be in right envelope.
Let us consider all the favorable outcomes
Step 2:
(i) 1 letter in correct envelope and 2 in wrong envelope.
(ie) $(E_1L_1,E_2L_3,E_3L_2),(E_1L_3,E_2L_2,E_3L_1),(E_1L_2,E_2L_1,E_3L_3)$
(ii) Two letter in correct envelope.
(ie) $(E_1L_1,E_2L_2,E_3L_3)$
$\therefore$ No of favorable outcomes =4
Step 3:
Total no of outcomes =$3!=3\times 2\times 1=6$
$\therefore$ Required probability =$\large\frac{n(E)}{n(S)}$
$\Rightarrow \large\frac{4}{6}$
$\Rightarrow \large\frac{2}{3}$
Hence (A) is the correct answer.
answered Jul 2, 2014 by sreemathi.v

Related questions

Ask Question
student study plans
JEE MAIN, CBSE, AIPMT Mobile and Tablet App
The ultimate mobile app to help you crack your examinations
Get the Android App