A math quiz has 5 multiple choice questions and each question has 3 choices. If a student has to guess (and is not able to remove any of the incorrect choices) what is the probability that the student answers all the questions correctly?
To find the probability that the student answers all the questions correctly by guessing, we need to calculate the probability of guessing the correct answer for each question and then multiply those probabilities together.
Since each question has 3 choices and only 1 correct answer, the probability of guessing the correct answer for each question is 1/3.
Therefore, the probability of answering all 5 questions correctly by guessing is:
(1/3) * (1/3) * (1/3) * (1/3) * (1/3) = 1/243
So, the probability that the student answers all the questions correctly by guessing is 1/243 or approximately 0.41%.