InterviewSolution
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InterviewSolution
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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)`, isA. `(1)/(2)`B. `(1)/(2^(n)-1)`C. `(1)/(2^(n))`D. `(1)/(3^(n))` |
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Answer» Correct Answer - B The set A has `2^(n)` elements. Therefore, two subsets P and Q can be chosen in `2^(n) C_(2)` ways. Suppose P consists of r elements. Then, P can be chosen in `.^(n)C_(r )`. 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. `therefore` Number of ways of selecting P and Q such that `Q=overline(P)` is `(1)/(2) underset(r=0)overset(n)sum .^(n)C_(r )=2^(n-1)` Hence, required probability `=(2^(n-1))/(.^(2n)C_(2))=(1)/(2^(n)-1)` |
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