Question

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?

• A. $\frac{1}{16}$
• B. $\frac{3}{16}$
• C. $\frac{1}{32}$
• D. $\frac{3}{32}$

Answer 1

Answer: (B)

n = total number of ways = $2^5 \, = 32$
Since each answer can be true or false & m = favourable number of ways
$= ^5C_4 \, +^5C_5$
$=\frac{5!}{4!1!} + \frac{5!}{5!0!} =5+1=6 \, \Rightarrow \, m = 6$
Since to pass the quiz, student must give 4 or 5 true answers
Hence, $P = \frac{m}{n} \, \Rightarrow \, p = \frac{6}{32} \, \, \Rightarrow \, \, P = \frac{3}{16}$