Question

4. (5pts) At MCPHS university, there are three mathematics courses: Algebra (A), Calculus (C), and Statistics (S). Records show that 45% of students take A, 35% take C, 30% take S, 10% take both A and C, 8% take A and S, 5% take C and S, and 3% take A, C, and S.

a. Find the probability of those who only take A.

b. Find the probability of those who only take one mathematics course.

c. Find the probability of those who take at least one mathematics course.

d. Find the probability of those who did not take any mathematics course.

Answer 1

a) P(only A) = P(A) - P(A and C) - P(A and S) + P(A, C and S)

                    = 0.45 - 0.1 - 0.08 + 0.03

                    = 0.3

b) P(only C) = P(C) - P(C and A) - P(C and S) + P(A, C and S)

                    = 0.35 - 0.1 - 0.05 + 0.03

                    = 0.23

P(only S) = P(S) - P(S and A) - P(C and S) + P(A, C and S)

                = 0.3 - 0.08 - 0.05 + 0.03

                = 0.2

P(only one mathematics course) = P(only A) + P(only C) + P(only S)

                                                     = 0.3 + 0.23 + 0.2

                                                     = 0.73

c) P(at least one) = P(A U C U S)

                            = P(A) + P(C) + P(S) - P(A and C) - P(A and S) - P(C and S) + P(A, C and S)

                            = 0.45 + 0.35 + 0.3 - 0.1 - 0.08 - 0.05 + 0.03

                            = 0.9

d) P(did not take any course) = 1 - P(at least one course)

                                                = 1 - 0.9

                                                = 0.1