Question

A pop quiz consists of three true–false questions and three multiple choice questions. Each multiple choice question has five possible answers. If a student blindly guesses the answer to every question, what is the probability that the student will correctly answer all six questions? (Round your answer to 3 decimal places.) Probability

Answer 1

Answer: 0.001

Step-by-step explanation:

Given : Number of true–false questions  =3

Choices of answer for true–false questions =2

Then , probability that the answer is correct for a true–false question =$\dfrac{1}{2}=0.5$

Also, Number of multiple choice questions  =3

Choices of answer for multiple choice questions = 5

Then , probability that the answer is correct for a multiple choice question =$\dfrac{1}{5}=0.2$

Now, the probability that the student will correctly answer all six questions :-

$(0.2)^3\times(0.5)^3=0.001$

Hence, the probability that the student will correctly answer all six questions = 0.001