Question

A student is given a true-false exam with $10$ question. If he gets $8$ or more correct answers, he passes the exam. Given that he guesses at the answer to each question, the probability that he passes the exam, is

• A. $\frac{6}{128}$
• B. $\frac{9}{128}$
• C. $\frac{7}{128}$
• D. none of these

Answer 1

The correct option is C $\frac{7}{128}$

$n=$ total number of ways $=2^{10}=1024$
Since each answer can be true or false.
and $m=$ favorable number of ways ${=}^{10}{C}_8{+}^{10}{C}_9{+}^{10}{C}_{10}=45+10+1=56$
Since to pass the exam, he must give $8$ or $9$ or $10$ true answers,
Hence, $p=\frac{m}{n}=\frac{56}{1024}=\frac{7}{128}$