Question

Amanda is taking a quiz that consists of five multiple choice questions, each having three answers from which to choose. If she guesses on each question, what's the probability that Amanda will get 100% on the quiz?

Answer 1

0.41%

Explanation:

He have 5 questions which are independent of each other, this means, that the probability of having one question correct does not depend on the probability of having other questions correct. Thus, we know that the probability of having all the questions correct when guessing is equal to the product of the probabilities of having each question correct:

P(all correct)=P(1st correct)*P(2nd correct)*P(3rd correct)*P(4th correct)*P(5th correct)

As every questions have 3 options and Amanda is guessing, her probability in each questions is 1/3. So:

P(all correct)=(1/3)*(1/3)*(1/3)*(1/3)*(1/3)= (1^5) / (3^5) = 1/243 = 0.0041 = 0.41%

So, the probability of having all questions correct is 0.41% when guessing.