On a multiple-choice quiz (not this one), there are 5 questions with 3 choices each. Each question has only one correct answer. If a student randomly guesses on all of the questions, what is the probability that the student will get at least one question wrong? 99.59\% \( 86.83 \% \) 13.17\% \( 0.41 \% \)

To find the probability that a student will get at least one question wrong, we first calculate the probability of getting all questions right. The probability of guessing a question correctly is \( \frac{1}{3} \). Since there are 5 questions, the probability of getting all questions right is \( \left( \frac{1}{3} \right)^5 = \frac{1}{243} \). Therefore, the probability of getting at least one question wrong is \( 1 - \frac{1}{243} \), which is approximately \( 0.9959 \) or \( 99.59\% \). So, the answer is \( 99.59\% \)! If you think about it, each question is like a little game of chance. Just as in a game, sometimes luck isn't on your side, and that can lead to surprising outcomes. The more questions you have, the more chances for that twist ending! So next time you're faced with a multiple-choice quiz, remember that even if you feel lost, you have a solid chance of getting at least one answer wrong when guessing randomly. It’s all math! Now, if you're working on multiple-choice questions regularly, aiming for familiarity could be your best strategy. Practice various types of questions, and you might find patterns that help with your guessing! Just make sure not to rely solely on guessing; that’s the biggest mistake! Balancing luck with knowledge boosts confidence and scores.