JEE Mains · Maths · STD 12 - 13. probability
let \(S = \{1, 2, … 20\}\). A subset \(B\) of \(S\) is said to be \(“nice”\), if the sum of the elements of \(B\) is \(203\). Then the probability that a randomly chosen subset of \(S\) is \(‘nice’\) is
- A \(\frac{7}{{{2^{20}}}}\)
- B \(\frac{5}{{{2^{20}}}}\)
- C \(\frac{4}{{{2^{20}}}}\)
- D \(\frac{6}{{{2^{20}}}}\)
Answer & Solution
Correct Answer
(B) \(\frac{5}{{{2^{20}}}}\)
Step-by-step Solution
Detailed explanation
Sum of all elements of \(S=210\) So \(X\) be a nice set if \(x=\{S-\{7\}, S-\{1,6\}, S-\{2,5\}, S-\{3,4\}, S-\{1,2,4\}\}\) \(P(x)=\frac{5}{2^{20}}\) \(\therefore(2)\) is the answer.
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