JEE Mains · Maths · STD 11 - 14. probability
A set \(S\) contains \(7\) elements. A non-empty subset \(A\) of \(S\) and an element \(x\) of \(S\) are chosen at random. Then the probability that \(x \in A\) is
- A \(\frac{1}{2}\)
- B \(\frac{64}{127}\)
- C \(\frac{63}{128}\)
- D \(\frac{31}{128}\)
Answer & Solution
Correct Answer
(B) \(\frac{64}{127}\)
Step-by-step Solution
Detailed explanation
Let \(\mathrm{S}=\left\{x_{1}, x_{2}, x_{3}, x_{4}, x_{5}, x_{6}, x_{7}\right\}\) Let the chosen element be \(x_{i}\), Total number of subsets of \(S=2^{7}=128\) No. of non-empty subsets of \(S=128-1\) \(=127\) We need to find number of those subsets that contains \(x_{i}\),…
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