Option A: 11.8%
Step-by-step explanation:
The total number of question n=10
The probability of getting true is 
The probability of getting false is 
It is given that the student gets 7 out of 10 questions right, the, 
Using binomial distribution formula,
![P(x)=\left[\frac{n !}{x !(n-x) !}\right] p^{x} q^{n-x}](https://tex.z-dn.net/?f=P%28x%29%3D%5Cleft%5B%5Cfrac%7Bn%20%21%7D%7Bx%20%21%28n-x%29%20%21%7D%5Cright%5D%20p%5E%7Bx%7D%20q%5E%7Bn-x%7D)
Substituting the values, we get,
![\begin{aligned}P(7) &=\left[\frac{10 !}{7 !(10-7) !}\right]\left(\frac{1}{2}\right)^{7}\left(\frac{1}{2}\right)^{3} \\&=\left[\frac{10 !}{7 ! 3 !}\right]\left(\frac{1}{2}\right)^{7+3}\end{aligned}](https://tex.z-dn.net/?f=%5Cbegin%7Baligned%7DP%287%29%20%26%3D%5Cleft%5B%5Cfrac%7B10%20%21%7D%7B7%20%21%2810-7%29%20%21%7D%5Cright%5D%5Cleft%28%5Cfrac%7B1%7D%7B2%7D%5Cright%29%5E%7B7%7D%5Cleft%28%5Cfrac%7B1%7D%7B2%7D%5Cright%29%5E%7B3%7D%20%5C%5C%26%3D%5Cleft%5B%5Cfrac%7B10%20%21%7D%7B7%20%21%203%20%21%7D%5Cright%5D%5Cleft%28%5Cfrac%7B1%7D%7B2%7D%5Cright%29%5E%7B7%2B3%7D%5Cend%7Baligned%7D)
Solving, we get,


To find the probability, multiply it by 100, we get,
%
Thus, the correct answer is 11.8%