AP EAMCET · Maths · Probability
If two subsets \(\mathrm{A}\) and \(\mathrm{B}\) are selected at random from a set \(\mathrm{S}\) containing \(\mathrm{n}\) elements, then the probability that \(\mathrm{A} \cap \mathrm{B}\) \(=\phi\) and \(\mathrm{A} \cup \mathrm{B}=\mathrm{S}\), is
- A \(\frac{1}{2^n}\)
- B \(2^n\)
- C \(\frac{1}{2^{\mathrm{n}+1}}\)
- D \(\frac{1}{2^n \times 2^n}\)
Answer & Solution
Correct Answer
(A) \(\frac{1}{2^n}\)
Step-by-step Solution
Detailed explanation
Given that \(S\) contains \(n\) elements and two sets \(A\) and \(B\) are selected. Two set \(A\) and \(B\) can be selected in \(2^n\) ways. The no. of ways of selecting two sets such that their union is \(S\) and intersection is \(2^n\). Therefore the probability…
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