Final answer:
To determine the probability of a student passing a 10-question true-false quiz by randomly guessing to get at least 70 percent correct, we must calculate the probabilities of getting 7, 8, 9, or 10 answers correct using the binomial probability formula and sum them up.
Step-by-step explanation:
When a student is taking a 10-question true-false quiz and guesses randomly on each answer, the probability of answering any given question correctly is 0.5 (since there are only two possible answers: true or false, which makes it a 50/50 chance). To pass the quiz with a grade of at least 70 percent, the student needs to get at least 7 questions right.
The probability of getting exactly k questions right out of 10 can be calculated using the binomial probability formula, which is P(X=k) = (n choose k) * p^k * (1-p)^(n-k), where 'n' is the number of trials (10 in this case), 'k' is the number of successful trials, and 'p' is the probability of success on a single trial (0.5 here). In this case, we need to calculate this for getting 7, 8, 9, or 10 questions correct.
Once we have these probabilities, we can sum them up to get the total probability of passing the test:
Probability of passing = P(X=7) + P(X=8) + P(X=9) + P(X=10).
Let's calculate the probabilities using the formula for P(X=7), P(X=8), P(X=9), and P(X=10) and then add them to determine the total probability of passing.