Final answer:
The probability of a student passing a 10-question true-false quiz with at least 70 percent by guessing randomly requires calculating the sum of the probabilities of getting 7, 8, 9, and 10 questions correct. This is determined by using the binomial probability formula for each case and summing the results.
Step-by-step explanation:
To calculate the probability of a student passing a true-false quiz with at least a 70 percent score, we need to determine the likelihood of the student getting 7 or more questions correct out of 10 when guessing randomly. For true-false questions, the probability of getting a question correct by guessing is 0.5. To pass the quiz with at least a 70 percent score, the student needs to get at least 7 questions correct.
Using binomial probability, we can calculate the probability of getting exactly k correct answers out of n questions, with a success probability p for each question:
P(X = k) = (n choose k) * p^k * (1-p)^(n-k)
Here 'n choose k' represents the binomial coefficient, which calculates the number of ways to choose k successes from n trials. The probability of getting at least 7 correct answers is the sum of the probabilities of getting 7, 8, 9, and 10 correct answers:
- P(X ≥ 7) = P(X = 7) + P(X = 8) + P(X = 9) + P(X = 10)
The calculation involves determining these four probabilities and summing them. Because the exact binomial probabilities are beyond the scope of this response due to their complexity, students are typically encouraged to use statistical software or binomial probability tables.
In conclusion, the higher the number of questions marked correctly, the higher the final exam score will likely be. However, keep in mind that guessing on a quiz is not a reliable strategy for success and generally leads to lower scores.