# NCERT Class 11 Mathematics Solutions: Chapter 16 –Probability Miscellaneous Exercise Part 3

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1. 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.

Answer:

Consider, be three letters and be their corresponding envelops respectively.

There are ways of inserting letters in envelops.

These are as follows:

There are ways in which at least one letter is inserted in a proper envelope.

So, the required probability

2. A and B are two events such that and . Find

(i)

(ii)

(iii)

(iv)

Answer:

It is given that

Answer: (i)

We know that

Answer: (ii)

[by De Morgan’s law]

Answer: (iii)

Answer: (iv)