Final answer:
The correct answer is that the probability of the student passing the quiz by randomly guessing is less than 100 percent. This is calculated using the binomial probability formula.
Step-by-step explanation:
The probability of a student passing a 10-question true-false quiz by guessing each answer and achieving at least a 70 percent can be calculated as the sum of the probabilities of getting exactly 7, 8, 9, or 10 questions correct. Since there are two options for each question (true or false), the probability of guessing one question correctly is 1/2. To pass the quiz with at least 70 percent, the student needs to get at least 7 out of 10 questions correct.
To find this probability, we use the binomial probability formula which is given by P(X=k) = C(n,k) * p^k * (1-p)^(n-k), where C(n, k) is the combination of n things taken k at a time, p is the probability of success on a single trial, and k is the number of successes.
When we calculate the probabilities for each of these cases (getting exactly 7, 8, 9, or 10 correct) and sum them up, we will find that the probability of passing the quiz is definitely less than 100 percent but not 0 percent. Therefore, the correct answer is b. It would be less than 100 percent.