Question

The probability of answering $6$ out of $10$ questions correctly in a true or false examination is

• A. ${}^{10}{C}_4{\left(\frac{1}{2}\right)}^4$
• B. ${}^{10}{C}_6{\left(\frac{1}{2}\right)}^6$
• C. ${}^{10}{C}_6{\left(\frac{1}{2}\right)}^{10}$
• D. ${}^{10}{C}_6{\left(\frac{1}{2}\right)}^8$

Answer 1

The correct option is C ${}^{10}{C}_6{\left(\frac{1}{2}\right)}^{10}$

Probability of answering a question correctly in a true or false questionnaire is $\frac{1}{2}$.
Hence, for $10$ questions, the probability of answering $6$ of them correctly is
${}^{10}{C}_6\left(\frac{1}{2}{)}^6\right(1-\frac{1}{2}{)}^4$
$={}^{10}{C}_6(\frac{1}{2}{)}^{10}$