Final answer:
To calculate the probability of a student passing a true-false quiz by guessing, the binomial probability formula is used. The student must guess at least 7 of the 10 questions correctly to pass with a 70%. The probability of each successful outcome is summed for the final answer.
Step-by-step explanation:
The probability of a student passing a 10-question true-false quiz with at least a 70 percent without studying implies the student needs to guess correctly on at least 7 out of the 10 questions. On any given true-false question, the probability of guessing correctly is 0.5 since there are only two possible outcomes, each equally likely. To pass the quiz, the student needs to correctly guess either 7, 8, 9, or all 10 questions correctly. Using the binomial probability formula, we calculate the probabilities for each of these outcomes and sum them to find the total probability of passing.
The binomial probability formula is P(X = k) = (n choose k) * p^k * (1-p)^(n-k), where 'n' is the number of trials, 'k' is the number of successful trials, and 'p' is the probability of success on any given trial. In this scenario, 'n' equals 10, 'k' will be 7, 8, 9, or 10, and 'p' equals 0.5. The sum of the probabilities of these four outcomes will give us the desired probability of the student passing the quiz.
Studying, time management, and reviewing your quiz results are essential steps to ensure you don't run out of time during a quiz and can improve upon past performance.