Final answer:
The subject is Mathematics at a High School level, dealing with probability concepts. For Helen's free throws, the probability that she makes both is 63.75%. The true-false quiz question would require a binomial probability calculation, though specific figures are not provided for a complete answer.
Step-by-step explanation:
The subject of this question is Mathematics, and the grade level would be High School since it involves understanding the concept of probability, which is typically covered at this education level. Let us look at two questions from the information provided.
For Helen's basketball free throws, we are given that the probability she makes the first shot, P(C), is 0.75, and the probability she makes the second shot, P(D), is also 0.75. The probability that she makes the second free throw given that she made the first is 0.85.
To find the probability that Helen makes both free throws, we would multiply the probability of her making the first shot by the probability of her making the second given she made the first: P(C) * P(D given C) = 0.75 * 0.85 = 0.6375 or 63.75%.
Regarding the probability of passing a true-false quiz with random guessing, a student would need to get at least 7 out of 10 questions correct for a 70 percent grade. Since the answers are randomly guessed, the probability of getting each question right is 0.5.
To find the probability of getting at least 7 questions right, we would need to use the binomial probability formula. However, we aren't provided with enough detail to calculate this probability in your query. Generally, this would involve summing the probabilities of getting exactly 7, exactly 8, exactly 9, and exactly 10 questions correct.