Final answer:
To determine the probability of passing a true-false quiz by guessing, you calculate the combined probabilities of correctly guessing at least 7 out of 10 questions. This involves using the binomial probability formula or a statistical calculator to find the sum of the probabilities for 7, 8, 9, and 10 correct answers.
Step-by-step explanation:
The question at hand is determining the probability of passing a true-false quiz without studying. In a 10-question quiz, achieving at least a 70 percent means getting at least 7 questions correct. Each question has a 50 percent chance of being answered correctly if guessed randomly, because there are only two possible answers: true or false. To calculate the probability of getting at least 7 out of 10 questions correct by guessing, you can use the binomial probability formula, considering the successes (correct answers) and failures (incorrect answers).
We are dealing with a binary outcome here (true or false), and the student is guessing, so each outcome is equally likely. The probability of exactly 7 correct guesses is determined by the combination of 10 questions taken 7 at a time, multiplied by the probability of getting 7 questions right and 3 questions wrong. However, since we are looking for at least 7 correct answers, we must also consider the probabilities of getting exactly 8, 9, or 10 correct answers and add those probabilities together. This calculation can become quite complex and might be best approached using a binomial probability distribution table or a calculator designed for statistical analysis.
Keep track of the time, and review your results after submitting your quiz. Studying efficiently and thoroughly will prepare you for a proctored exam and contribute to better time management and overall higher quiz scores.