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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?
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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, $p=\frac{m}{n} \Rightarrow p=\frac{6}{32} \Rightarrow p=\frac{3}{16}$
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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