Question

Three letters are written to three different persons and addresses on the three envelopes are also written. Without looking in the addresses, the letters are kept in these envelopes. The probability that all the letters are not placed into their right envelopes is :

A. $$\frac{1}{2}$$
B. $$\frac{1}{3}$$  
C. $$\frac{1}{6}$$
D. $$\frac{5}{6}$$
Answer :   $$\frac{1}{3}$$
Solution :
$$\eqalign{ & {\text{Favourable ways}} = 3!\left( {1 - \frac{1}{{1!}} + \frac{1}{{2!}} - \frac{1}{{3!}}} \right) = 2 \cr & {\text{Total ways}} = 3! \cr & \therefore \,{\text{Required probability}} = \frac{2}{{3!}} = \frac{1}{3} \cr} $$

Releted MCQ Question on
Statistics and Probability >> Probability

Releted Question 1

Two fair dice are tossed. Let $$x$$ be the event that the first die shows an even number and $$y$$ be the event that the second die shows an odd number. The two events $$x$$ and $$y$$ are:

A. Mutually exclusive
B. Independent and mutually exclusive
C. Dependent
D. None of these
Releted Question 2

Two events $$A$$ and $$B$$ have probabilities 0.25 and 0.50 respectively. The probability that both $$A$$ and $$B$$ occur simultaneously is 0.14. Then the probability that neither $$A$$ nor $$B$$ occurs is

A. 0.39
B. 0.25
C. 0.11
D. none of these
Releted Question 3

The probability that an event $$A$$ happens in one trial of an experiment is 0.4. Three independent trials of the experiment are performed. The probability that the event $$A$$ happens at least once is

A. 0.936
B. 0.784
C. 0.904
D. none of these
Releted Question 4

If $$A$$ and $$B$$ are two events such that $$P(A) > 0,$$   and $$P\left( B \right) \ne 1,$$   then $$P\left( {\frac{{\overline A }}{{\overline B }}} \right)$$  is equal to
(Here $$\overline A$$ and $$\overline B$$ are complements of $$A$$ and $$B$$ respectively).

A. $$1 - P\left( {\frac{A}{B}} \right)$$
B. $$1 - P\left( {\frac{{\overline A }}{B}} \right)$$
C. $$\frac{{1 - P\left( {A \cup B} \right)}}{{P\left( {\overline B } \right)}}$$
D. $$\frac{{P\left( {\overline A } \right)}}{{P\left( {\overline B } \right)}}$$

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