Final answer:
The probability of a student passing a true-false quiz by random guessing is obtained by summing the probabilities of getting at least 7 out of 10 questions correct. Since the probability of correctly guessing each question is 1/2, the binomial probability formula is used to calculate the probabilities for getting 7, 8, 9, or 10 questions correct.
Step-by-step explanation:
To determine the probability of a student passing a 10-question true-false quiz by guessing randomly at each answer and achieving at least a 70 percent score, we must first understand that a 70 percent score on a 10-question quiz means getting at least 7 out of 10 questions correct.
Since each question is true-false, there's a 1/2 chance of getting any single question correct by random guessing. To find the probability of getting exactly 7, 8, 9, or 10 questions correct, we apply the binomial probability formula, which in this case is P(X=k) = (nCk) * (p^k) * (q^(n-k)), where 'n' is the total number of questions, 'k' is the number of questions answered correctly, 'p' is the probability of getting a question right, and 'q' is the probability of getting a question wrong.
The student needs to get at least 7 questions right, so we must calculate probabilities for all outcomes where the student gets 7, 8, 9, or 10 questions right and add them together to find the total probability of passing the quiz.