Option A: 11.8%
Step-by-step explanation:
The total number of question n=10
The probability of getting true is [tex]p=\frac{1}{2}[/tex]
The probability of getting false is [tex]q=\frac{1}{2}[/tex]
It is given that the student gets 7 out of 10 questions right, the, [tex]x=7[/tex]
Using binomial distribution formula,
[tex]P(x)=\left[\frac{n !}{x !(n-x) !}\right] p^{x} q^{n-x}[/tex]
Substituting the values, we get,
[tex]\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}[/tex]
Solving, we get,
[tex]P(7)=\frac{15}{128}[/tex]
[tex]P(7)=0.118[/tex]
To find the probability, multiply it by 100, we get,
[tex]0.118*100=11.8[/tex]%
Thus, the correct answer is 11.8%
