Final answer:
The probability of a student passing a 10-question true-false test by guessing can be found by calculating the sum of the probabilities of getting at least 7 out of 10 questions correct via the binomial probability formula.
Step-by-step explanation:
To calculate the probability of the student scoring at least a 70 percent on a 10-question true-false quiz by guessing, we need to determine the number of ways the student can correctly answer at least 7 out of 10 questions. Since each question has only two possible answers (true or false), there is a 50 percent chance, or probability of 0.5, of guessing any single question correctly.
We apply 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 (questions), 'k' is the number of successful outcomes (correct answers), and 'p' is the probability of success on a single trial. To pass the quiz with a minimum score of 70 percent, the student needs to get at least 7 of 10 questions correct.
We calculate the probability for getting exactly 7, 8, 9, or 10 questions correct and sum these probabilities:
- P(X=7) = (10 choose 7) * 0.5^7 * 0.5^3
- P(X=8) = (10 choose 8) * 0.5^8 * 0.5^2
- P(X=9) = (10 choose 9) * 0.5^9 * 0.5^1
- P(X=10) = (10 choose 10) * 0.5^10
Then, add these probabilities together to find the total probability of passing the test.