Final answer:
The question is about finding the probability of a student passing a true-false quiz by randomly guessing on each question to achieve a 70 percent score. The probability can be calculated using the binomial probability formula, considering the probability of getting 7 or more questions right out of 10.
Step-by-step explanation:
The question being asked is about the probability of a student passing a 10-question true-false quiz by guessing randomly on each answer and achieving at least a 70 percent score, which is equivalent to getting at least 7 out of 10 questions correct. In probability, we can calculate the chances of such an event using the concepts of binomial probability, as each question has two possible outcomes (true or false).
Given that each question can be answered correctly by chance with a probability of 0.5 (since there are two options), and we are trying to find the probability of getting at least 7 questions right, we must consider all the outcomes where the student gets 7, 8, 9, or 10 questions correct. We can use a binomial probability formula to calculate this, which is P(X = k) = (n choose k) * p^k * (1-p)^(n-k), where 'n' is the number of trials (10 questions), 'k' is the number of successful outcomes, and 'p' is the probability of success on a single trial (0.5)
The combined probability of getting 7, 8, 9, or 10 questions right is thus the sum of the individual probabilities for k=7, k=8, k=9, k=10.
Calculations using a binomial probability equation or a calculator would yield:
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- Probability of exactly 7 right answers: P(X = 7)
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- Probability of exactly 8 right answers: P(X = 8)
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- Probability of exactly 9 right answers: P(X = 9)
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- Probability of exactly 10 right answers: P(X = 10)
Summing these probabilities will give us the final answer to the question of the student's likelihood of passing the quiz.