Class 11
MATHS
Probability

# Let A be a set consisting of n elements. The probability of selecting two subsets P and Q of set A such that Q= overline(P), is

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Text Solution

(1)/(2)(1)/(2^(n)-1)(1)/(2^(n))(1)/(3^(n))

B
Solution :
The set A has 2^(n) elements. Therefore, two subsets P and Q can be chosen in 2^(n) C_(2) ways. <br> Suppose P consists of r elements. Then, P can be chosen in .^(n)C_(r ). <br> Since, Q=overline(P). Therefore, P and Q can be chosen in .^(n)C_(r ) ways. But, r can vary from 0 to n and P and Q can be interchanged also. <br> therefore Number of ways of selecting P and Q such that Q=overline(P) is <br> (1)/(2) underset(r=0)overset(n)sum .^(n)C_(r )=2^(n-1) <br> Hence, required probability =(2^(n-1))/(.^(2n)C_(2))=(1)/(2^(n)-1)

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Class 11th

Probability

Class 11th

Probability

Class 11th

Probability
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