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 incorrect answers) what is the probability that the student answers all the questions correctly?
The probability of guessing a single question correctly is 1/3, since there are 3 choices.
Since each question is independent of the others, the probability of guessing all 5 questions correctly is the product of the individual probabilities:
(1/3) * (1/3) * (1/3) * (1/3) * (1/3) = (1/3)^5 = 1/243
Therefore, the probability that the student answers all the questions correctly by guessing is 1/243.