Question

Suppose a quiz has 12 multiple choice questions. Each question has 4 answer choices. If a student takes the quiz and randomly guesses on every question.... Find the probability the student gets between 1 and 6, exclusive, questions correct.

Answer 1

The probability that the student gets between 1 and 6, exclusive, questions correct will be 0.7872...

Explanation

If the probability of success is $p$ , then the probability of $r$ successes in $n$ trials will be......

$P = ^nC_{r}*(p)^r (1-p)^n^-^r$

Here, the quiz has total 12 questions and each question has 4 answer choices. So, $n=12$ and $p=\frac{1}{4}= 0.25$

The student gets between 1 and 6, exclusive, questions correct. It means there can be 2 or 3 or 4 or 5 questions as correct. So....

The probability of 2 or 3 or 4 or 5 questions correct will be:

$=^1^2C_{2}*(0.25)^2(1-0.25)^1^0 + ^1^2C_{3}*(0.25)^3(1-0.25)^9 +^1^2C_{4}*(0.25)^4(1-0.25)^8+^1^2C_{5}*(0.25)^5(1-0.25)^7\\ \\ =0.2322...+0.2581...+0.1935...+0.1032... \\ \\ =0.7872...$