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Question: Answered & Verified by Expert
An unprepared student takes five-questions of true-false type quiz and guesses every answer. What is the probability that the student will pass the quiz if at least four correct answers is the passing grade?
MathematicsVector AlgebraVITEEEVITEEE 2006
Options:
  • A $\frac{1}{16}$
  • B $\frac{3}{16}$
  • C $\frac{1}{32}$
  • D $\frac{3}{32}$
Solution:
2738 Upvotes Verified Answer
The correct answer is: $\frac{3}{16}$
$\mathrm{n}=$ total number of ways $=2^{5}=32$
Since each answer can be true or false
$\& \mathrm{~m}=$ favourable number of ways
$\begin{array}{l}
={ }^{5} \mathrm{C}_{4}+{ }^{5} \mathrm{C}_{5} \\
=\frac{5 !}{4 ! 1 !}+\frac{5 !}{5 ! 0 !}=5+1=6 \Rightarrow \mathrm{m}=6
\end{array}$
Since to pass the quiz, student must give 4 or 5 true answers.
Hence, $p=\frac{m}{n} \Rightarrow p=\frac{6}{32} \Rightarrow p=\frac{3}{16}$

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