Final answer:
The probability of a student passing a 10-question true-false quiz by randomly guessing and getting at least 70 percent correct is obtained by calculating the binomial probability for getting 7, 8, 9, or 10 questions right and adding them together, which results in a low probability.
Step-by-step explanation:
Probability of Passing a True-False Quiz
To find the probability of a student passing a 10-question true-false quiz with at least a 70 percent by randomly guessing each answer, we need to calculate the chances of them getting at least 7 questions correct. Since each question has two possible answers, the probability of guessing one question correctly is 0.5. To pass with at least 70 percent, they need to guess at least 7 questions correctly. The probability of this event can be calculated using the binomial probability formula, which is P(X=k) = C(n,k) * p^k * (1-p)^(n-k), where C(n,k) is the number of combinations of n items taken k at a time, p is the probability of guessing one question right, and (1-p) is the probability of guessing one question wrong. In this case, n=10, k can be 7, 8, 9, or 10, and p=0.5. To find the total probability of getting at least 7 correct, we would add the probabilities for k=7, k=8, k=9, and k=10. Using this approach, we find that the probability is relatively low, showcasing the risks involved in relying on guesses rather than studying.