Final answer:
To determine the probability of a student passing a 10-question true-false exam by guessing, one must calculate the cumulative probability of answering at least 7 questions correctly using a binomial distribution. The waiting period for subsequent exam attempts after a failure is not specified and would depend on the specific exam and institution policies.
Step-by-step explanation:
To answer the question regarding the probability of a student passing a 10-question, true-false exam with at least a 70 percent by guessing, we need to calculate the probability of getting at least 7 answers correct. Since each question is true or false, the probability of guessing each correctly is 0.5. A binomial probability distribution can be used here, where the number of trials is 10 (the number of questions), the number of successes is at least 7 (to pass with 70 percent), and the probability of success on each trial is 0.5.
The probability of exactly k successes out of n trials in a binomial distribution is given by the formula which can be computed using combination calculations (n choose k) and raising the probability of success and failure to the respective number of successes and failures. However, since the student needs to pass with at least 70 percent, we need to find the cumulative probability of getting exactly 7, 8, 9, or 10 correct answers. The sum of these probabilities will give us the desired likelihood of passing the exam.
Regarding the question about waiting time before subsequent attempts after failing an exam, it is generally specific to the exam and the administering institution's policies. The information provided does not contain such details, so it is not possible to answer the question about the waiting period for retaking the exam without additional context. Exams policies can vary by subject, institution, and even by country.