JEE Mains · Maths · STD 11 - 14. probability
A multiple choice examination has \(5\) questions. Each question has three alternative answers of which exactly one is correct. The probability that a student will get \(4\) or more correct answers just by guessing is :
- A \(\frac{{17}}{{{3^5}}}\)
- B \(\;\frac{{13}}{{{3^5}}}\)
- C \(\;\frac{{11}}{{{3^5}}}\)
- D \(\;\frac{{10}}{{{3^5}}}\)
Answer & Solution
Correct Answer
(C) \(\;\frac{{11}}{{{3^5}}}\)
Step-by-step Solution
Detailed explanation
\(p=\frac{1}{3}, q=\frac{2}{3}\) \(^{5} \mathrm{C}_{4}\left(\frac{1}{3}\right)^{4} \cdot \frac{2}{3}+^{5} \mathrm{C}_{5}\left(\frac{1}{3}\right)^{5}\) \(=5 \cdot \frac{2}{3^{5}}+\frac{1}{3^{5}}=\frac{11}{3^{5}}\)
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