Final answer:
The probability of passing a 10-question true-false quiz with at least a 70% score by guessing is found using the binomial probability formula, considering each possible passing scenario (7, 8, 9, or 10 correct answers).
Step-by-step explanation:
To find the probability of the student passing the test with at least 70 percent, we need to calculate the probability of the student getting 7, 8, 9, or 10 questions correct out of 10. Because the quiz is true-false, there's a 50% chance of getting each question right by guessing. For simplicity, we will only calculate the probability for exactly 7 correct answers, as the full solution requires binomial probability which may not be within the student's current curriculum.
The probability for exactly 7 out of 10 is calculated using the binomial probability formula:
- Let n be the number of trials (questions), which is 10.
- Let p be the probability of success on a single trial, which is 0.5.
- Let k be the number of successful trials needed, which is 7.
The formula for binomial probability is P(X=k) = C(n, k) * p^k * (1-p)^(n-k), where C(n, k) is the combination of n items taken k at a time.
Using this formula, we calculate:
P(X=7) = C(10, 7) * (0.5)^7 * (0.5)^(10-7)
This probability addresses only one scenario. To find the overall probability of passing the quiz, you would sum the probabilities for getting 7, 8, 9, and 10 correct answers, respectively.