Final answer:
The probability of passing a 10-question true-false quiz with at least 70 percent correct by guessing is calculated by using the binomial probability formula for each number of correct answers that is equal to or greater than 7 and summing these probabilities.
Step-by-step explanation:
The student has asked about calculating the probability of passing a quiz with a certain percentage of correct answers while guessing randomly. To find the probability of passing a 10-question true-false quiz by guessing and achieving at least a 70 percent score, we need to calculate the probability of answering correctly 7, 8, 9, or all 10 questions. Since there are only two possible answers for each question (true or false), the probability of guessing correctly is 1/2.
Therefore, the probability of getting exactly 7 questions right is given by the binomial probability formula:
P(X=k) = nCk * p^k * (1-p)^(n-k)
where p is the probability of success (1/2), n is the number of trials (10), k is the number of successful trials (7), and nCk represents the combination of n items taken k at a time.
Using this formula, you calculate the probabilities for each possibly passing number of correct answers and sum these probabilities to get the total probability of passing the quiz.