Question

A student randomly guesses on 10 true or false questions use the bionomial model to find the probability that the student gets 7 out of the 10 questions right

Answer 1

Option A: 11.8%

Step-by-step explanation:

The total number of question n=10

The probability of getting true is $p=\frac{1}{2}$

The probability of getting false is $q=\frac{1}{2}$

It is given that the student gets 7 out of 10 questions right, the, $x=7$

Using binomial distribution formula,

$P(x)=\left[\frac{n !}{x !(n-x) !}\right] p^{x} q^{n-x}$

Substituting the values, we get,

$\begin{aligned}P(7) &=\left[\frac{10 !}{7 !(10-7) !}\right]\left(\frac{1}{2}\right)^{7}\left(\frac{1}{2}\right)^{3} \\&=\left[\frac{10 !}{7 ! 3 !}\right]\left(\frac{1}{2}\right)^{7+3}\end{aligned}$

Solving, we get,

$P(7)=\frac{15}{128}$

$P(7)=0.118$

To find the probability, multiply it by 100, we get,

$0.118*100=11.8$%

Thus, the correct answer is 11.8%