Final answer:
To pass a 10-question true-false quiz with at least a 70 percent by guessing, we calculate the probabilities of getting at least 7 out of 10 questions correct using the binomial probability formula, sum the outcomes, and recognize that the overall probability will be low.
Step-by-step explanation:
The question is asking about the probability of a student passing a true-false quiz by guessing on all answers. To pass with at least a 70 percent, the student needs to get at least 7 out of 10 questions correct. Since each question has two possible answers (true or false), the probability of guessing one question correctly is 1/2.
Passing the quiz by guessing would require the student to guess at least 7 questions correctly out of 10. We use the binomial probability formula to calculate this. The probability of exactly k successes in n trials is given by: P(X=k) = (n choose k) * p^k * (1-p)^(n-k), where p is the success probability for one trial, and (n choose k) is the binomial coefficient.
Since we're interested in probability of guessing exactly 7, 8, 9, or 10 correctly, we need to calculate these probabilities individually and then sum them up. However, without doing the calculations, we can conclude that the probability will be fairly low because there is only a 50% chance to get each question right and we need to get a high number of them correct. If we were to do all the calculations, we would sum up the probabilities of getting 7, 8, 9, and 10 questions correct to come up with the overall passing probability.