JEE Mains · Maths · STD 12 - 13. probability
A student appeared in an examination consisting of \(8\) true - false type questions. The student guesses the answers with equal probability. The smallest value of \(\mathrm{n}\), so that the probability of guessing at least \('n'\) correct answers is less than \(\frac{1}{2}\), is:
- A \(5\)
- B \(3\)
- C \(6\)
- D \(4\)
Answer & Solution
Correct Answer
(A) \(5\)
Step-by-step Solution
Detailed explanation
\(\mathrm{P}(\mathrm{E})<\frac{1}{2}\) \(\Rightarrow \sum_{r=n}^{8}{ }^{8} C_{r}\left(\frac{1}{2}\right)^{8-r}\left(\frac{1}{2}\right)^{r}<\frac{1}{2}\) \(\Rightarrow \sum_{r=n}^{8}{ }^{8} C_{r}\left(\frac{1}{2}\right)^{8}<\frac{1}{2}\)…
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