Final answer:
The student seeks to determine the probability of passing a true-false quiz by guessing the answers in order to achieve at least a 70% grade, which necessitates answering 7 or more questions correctly out of 10. A binomial probability formula or a binomial distribution table/calculator must be used to calculate the combined probability for all acceptable outcomes.
Step-by-step explanation:
The question posed by the student involves calculating the probability that they will pass a quiz by guessing the answers. To pass the quiz with at least a 70% grade, they must answer correctly at least 7 out of 10 questions on a true-false quiz. Since each question has two possible answers (true or false), the probability of guessing one question correctly is 1/2.
To find the probability of getting exactly 7, 8, 9, or 10 questions right by chance, we would use the binomial probability formula, which is P(x)=nCx * p^x * (1-p)^(n-x), where n is the total number of questions, x is the number of correct answers needed, p is the probability of getting one question right, and nCx is the combination of n items taken x at a time.
However, since you need to find the probability for at least 7 correct answers, you would sum the probabilities of getting exactly 7, exactly 8, exactly 9, and exactly 10 questions correct. This requires using the binomial theorem or a binomial distribution table/calculator.