Final answer:
The probability of a student passing a 10-question true-false quiz by guessing is found using the binomial probability formula, considering they need at least 7 out of 10 correct to pass.
Step-by-step explanation:
If a student guesses randomly on a true-false quiz, we can analyze the probability of them passing based on certain assumptions. For a 10-question quiz, with each question having two possible choices (true or false), the chance of guessing correctly is 1/2 for each question. When considering a passing mark of at least 70%, the student would need to answer correctly 7 out of 10 questions. To find the exact probability, we'd use the binomial probability formula:
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.
In this case, 'n' is 10, 'k' would need to be at least 7 to pass, and 'p' is 1/2. By calculating the binomial probabilities for 'k' equal to 7, 8, 9, and 10 and adding them together, you'd obtain the probability of passing the quiz.