Question

There are 30% of students currently taking AP Art History who have taken previous AP courses. St. Louis High School has only 3 of 15 students who have taken previous AP courses. Design a simulation to determine the probability of getting this number of students, who have taken previous AP courses, in a group this size. Which of the following assignments of the digits through 9 would be appropriate for modeling this situation?

A. Assign 0, 1, and 2 as having token previous AP courses and 3, 4, 5, 6,7,8, and 9 as not having taken previous AP courses
B. Assign 1, 2, 3, 4, and 5 as having taken previous AP courses and 6, 7, 8, and 9 as not having taken previous AP courses.
C. Assign 0 and 1 as having taken previous AP courses and 2, 3, 4, 5, 6, 7, 8, and 9 as not having taken previous AP courses
D. Assign 0, 1, 2, and 3 as having taken previous AP courses and 4, 5, 6, 7, 8, and 9 as not having taken previous AP courses.
E. Assign 6, 7, 8, and 9 as having taken previous AP courses and 0, 1, 2, 3, 4, and 5 as not having taken previous AP courses

Answer 1

The appropriate assignment of the digits in this situation would be option A. In option A, 0, 1, and 2 are assigned as having taken previous AP courses, while the remaining digits are assigned as not having taken previous AP courses. To determine the probability of getting 3 out of 15 students who have taken previous AP courses, we can use the binomial probability formula.

Step-by-step explanation:

The appropriate assignment of the digits in this situation would be option A. In option A, 0, 1, and 2 are assigned as having taken previous AP courses, while the remaining digits are assigned as not having taken previous AP courses.

To determine the probability of getting 3 out of 15 students who have taken previous AP courses, we can use the binomial probability formula. The formula is:

P(X = k) = C(n, k) * p^k * (1 - p)^(n - k)

Where:

• P(X = k) is the probability of getting exactly k successes
• C(n, k) is the number of combinations of choosing k successes out of n trials
• p is the probability of success in one trial
• n is the number of trials

In this case, n is 15 (the number of students) and p is 0.3 (the probability of a student having taken previous AP courses). Substituting these values into the formula, we get:

P(X = 3) = C(15, 3) * (0.3)^3 * (1 - 0.3)^(15 - 3)

Calculating this value will give us the probability of getting exactly 3 students who have taken previous AP courses.