Final answer:
To calculate the probability of the student passing the test by guessing, we use the binomial probability formula with a success probability of 0.5 for each question. The calculation will involve finding the probabilities for getting 7, 8, 9, and 10 correct answers out of 10 and summing these probabilities to determine the likelihood of achieving a passing score of at least 70 percent.
Step-by-step explanation:
The question provided by the student involves calculating the probability of a specific event, which is a topic within the subject of Mathematics. Specifically, the problem given is to determine the probability of a student guessing randomly on a 10-question true-false quiz and passing with at least a 70 percent score. A passing grade of 70 percent would mean getting at least 7 out of 10 questions correct.
In order to solve this problem, we must use the binomial probability formula, which is given by P(X=k) = C(n,k) * (p)^k * (1-p)^(n-k), where P(X=k) is the probability of getting k successes in n trials, C(n,k) is the combination of n things taken k at a time, p is the probability of a success on a single trial, and (1-p) is the probability of a failure on a single trial.
For a true-false question, the probability of guessing correctly (p) is 0.5, as there are only two possible outcomes. We want to find the probability of getting at least 7 correct answers, which means we need to calculate the probability for 7, 8, 9, and 10 correct answers and add them together. This will give us the overall probability that the student will pass the test with at least a 70 percent by guessing.