For Questions 2 3 A high school with 1000 students offers t

(For Questions 2 & 3) A high school with 1000 students offers two AP courses: Statistics and Calculus. There are 120 students in the Calculus class roster, and 80 students in the Statistics class roster. We also know that 40 students enroll in both courses.

2. Find the probability that a randomly selected student takes neither AP course. (Show work and write the answer in simplest fraction form)

3. Let event A be that a randomly selected student takes AP Statistics course, and event B be that a randomly selected student takes AP Calculus course. Are A and B independent? Are A and B disjoint? Please explain.

Solution

2)

Number of students who opted for either Statistics or Calculus = 120 + 80 -40 = 160

Therefore , the Number of students who didn\'t opted for either Statistics or Calculus = 1000-160 = 840

The probability that a randomly selected student takes neither AP course = 840/1000 = 21/25 Answer

3)

P(A) = 80/1000

P(B) = 120/1000

P( A and B) = 40/1000

P(A) * (B) != P ( A and B) . Hence not independent

A and B are not disjoint because they have 40 common sample cases.