Question

A group of 15 students is randomly selected from those taking AP Art History. Given that 30% of students currently taking AP Art History have taken previous AP courses, what is the probability that exactly 3 out of the 15 students in the group have taken previous AP courses?

A) 0.0103
B) 0.0892
C) 0.2508
D) 0.3138

Answer 1

The probability that exactly 3 out of the 15 students in the group have taken previous AP courses is approximately 0.3138.

Step-by-step explanation:

To find the probability that exactly 3 out of the 15 students in the group have taken previous AP courses, we can use the binomial probability formula. The formula for calculating the probability of x successes in n trials is:

P(x) = C(n, x) * p^x * q^(n-x)

where C(n, x) is the number of combinations of n items taken x at a time, p is the probability of success, and q is the probability of failure.

In this case, n = 15, x = 3, p = 0.30 (probability that a student taking AP Art History has taken previous AP courses), and q = 1 - p = 0.70.

Plugging in the values, we get:

P(3) = C(15, 3) * 0.30^3 * 0.70^(15-3)

Using a calculator to calculate the combination and the powers of p and q, we find that the probability is approximately 0.3138. Therefore, the correct answer is option D) 0.3138.