Final answer:
The question involves calculating the probability of a student passing a 10-question true-false quiz by guessing, with the goal of achieving at least 7 correct answers. The calculation uses the binomial probability formula to find the probabilities for getting exactly 7, 8, 9, or 10 questions right and summing these up.
Step-by-step explanation:
The subject in question is a probability problem from Mathematics, specifically in the area of combinatorics. The student attempts a 10-question, true-false quiz and guesses each answer, aiming for at least 70 percent correct to pass. The student needs to guess correctly on at least 7 out of 10 questions.
To calculate this probability, we use the binomial probability formula:
First, determine the probability of getting exactly 7 questions correct.
Then calculate the same for 8, 9, and 10 correct answers.
Finally, sum up these probabilities to get the total probability of passing the quiz.
The formula for the binomial probability of getting exactly k successes in n trials is given by:
P(X=k) = C(n, k) * (p^k) * ((1-p)^(n-k))
Where:
C(n, k) is the binomial coefficient, representing the number of combinations of n things taken k at a time.
p is the probability of success on a single trial, and in this case, it is 0.5 since the quiz is true-false.
k is the number of successes we're checking for (7, 8, 9, or 10).
n is the total number of trials or questions in the quiz.
This calculation will provide an answer to what the probability is that the student passes by guessing and achieving at least a 70 percent grade.