Final answer:
The probability of a student passing a 10-question true-false quiz with at least a 70% score by guessing is the cumulative probability of guessing exactly 7, 8, 9, or 10 answers correctly. Since each question has only two possible answers, and without any prior knowledge, the chance of passing by guessing is low.
Step-by-step explanation:
The question posed is related to the concept of probability. Specifically, it deals with the case of a student attempting to pass a 10-question true-false quiz by guessing. Each question, therefore, has a 50% chance of being answered correctly just by chance. To pass the quiz with at least a 70% score, the student needs to answer at least 7 out of the 10 questions correctly.
To find the probability of getting exactly 7 out of 10 questions right by guessing, we can use the binomial probability formula which is P(x) = nCx * p^x * (1-p)^(n-x), where n is the number of trials, x is the number of successes, p is the probability of success on a single trial, and nCx is the binomial coefficient. In this scenario, the probability of getting at least 7 correct by guessing, P(X ≥ 7), is the sum of probabilities for getting exactly 7 right, exactly 8 right, exactly 9 right, and all 10 right.
However, calculating this by hand can be tedious, and it's often easier to use a statistical calculator or software to find the cumulative probability. Nevertheless, we can state that the probability of passing the test with a 70% grade by random guessing is relatively low given that the majority of outcomes involve getting less than 70% correct.