Let S be a set containing n elements and we select 2 subsets A and B of S at random then probability

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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

${2^n}$

${n^2}$

$1/n$

$1/{2^n}$

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

A fair coin and an unbiased die are tossed. Let $A$ be the event ' head appears on the coin' and $B$ be the event ' $3$ on the die'. Check whether $A$ and $B$ are independent events or not.

medium

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easy

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medium

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normal

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