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14.Probability
hard
Let $S$ be a set containing n elements and we select $2$ subsets $A$ and $B$ of $S$ at random then the probability that $A \cup B = S$ and $A \cap B = \phi $ is
A
${2^n}$
B
${n^2}$
C
$1/n$
D
$1/{2^n}$
Solution
(d) Ways of selection two subset of $A = {({2^n})^2}$
Ways of selection $A \cup B$ and $A \cap B$ are ${2^n}$
$\therefore$ Required probability $ = \frac{{{\rm{favourable \,\,cases}}}}{{{\rm{total \,\,cases}}}} = \frac{{{2^n}}}{{{{({2^n})}^2}}} = \frac{1}{{{2^n}}}$.
Standard 11
Mathematics
