MHT CET · Maths · 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 at least one correct answer is
- A \(\frac{80}{243}\)
- B \(\frac{32}{243}\)
- C \(\frac{163}{243}\)
- D \(\frac{211}{243}\)
Answer & Solution
Correct Answer
(D) \(\frac{211}{243}\)
Step-by-step Solution
Detailed explanation
There are 5 questions and each question has 3 options of which one is correct. \(\therefore\) Probability of getting correct answer \(=\frac{1}{3}\)
Thus \(\mathrm{n}=5, \mathrm{p}=\frac{1}{3}, \mathrm{q}=\frac{2}{3}\)
\(P\) (at least one correct answer)
\(=1-P(\) None is correct \()\)
\(=1-{ }^{5} C_{0}\left(\frac{1}{3}\right)^{0}\left(\frac{2}{3}\right)^{5}=1-1 \times 1 \times \frac{32}{243}\) \(=\frac{243-32}{243}=\frac{211}{243}\)
Thus \(\mathrm{n}=5, \mathrm{p}=\frac{1}{3}, \mathrm{q}=\frac{2}{3}\)
\(P\) (at least one correct answer)
\(=1-P(\) None is correct \()\)
\(=1-{ }^{5} C_{0}\left(\frac{1}{3}\right)^{0}\left(\frac{2}{3}\right)^{5}=1-1 \times 1 \times \frac{32}{243}\) \(=\frac{243-32}{243}=\frac{211}{243}\)
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