Question

A student takes a ten-question true-false quiz, but did not study and randomly guesses each answer. Find the probability that the student passes the quiz with a grade of at least $70\%$of the questions correct.

Short answer

The probability of having$70\%$answer is$0.11719$

Step-by-step solution

Given information 

The probability of success (POS) is a statistical concept that is widely utilized in the pharmaceutical business, as well as by health authorities, to aid decision-making.

The concept of probability of success is directly tied to conditional and predictive capacity.

Explanation 

The number of correct answers will be represented by a variable $X$.

With $12$trials and a probability of $0.5$, $X$has a binomial distribution.

Students must correctly answer $7$questions in order to receive an $70\%$accurate response. As a result, the desired probability is,

$$\begin{gathered} P(X=7)=\left(\begin{array}{c}10\\ 7\end{array}\right)0.5^{10} \\ =0.11719 \end{gathered}$$