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...

Step-by-step 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=(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...`