In a large introductory statistics lecture hall, the professor reports that 53% of the students enrolled have never taken a calculus course, 27% have taken only one semester of calculus, and the rest have taken two or more semesters of calculus. The professor randomly assigns students to groups of three to work on a project for the course. You are assigned to be part of a group. What is the probability that of your other two groupmates, a) neither has studied calculus? b) both have studied at least one semester of calculus? c) at least one has had more than one semester of calculus?

a) neither has studied calculus = 0.2809

b) both have studied at least one semester of calculus = 0.2209

c) at least one has had more than one semester of calculus = 0.36

Step-by-step explanation:

From the question, the amount of students that have never taken calculus course is 53%.

The amount of students that have taken only one semester of calculus is 27%.

Since the rest have taken two or more semesters of calculus, The amount of students that have taken two or more semesters of calculus = 100% - (53 + 27)%  = 100% - 80% = 20%

Therefore the probability that a student has studied calculus for two or more semesters = 0.2

The probability that a student has studied some calculus = 0.27 + 0.2 = 0.47

The probability that a student has studied no more than one semester of calculus = 0.53 + 0.27 = 0.8

What is the probability that of your other two group mates:

a) neither has studied calculus

The probability that neither has studied calculus = 0.53 × 0.53 = 0.2809

b) both have studied at least one semester of calculus

The probability that both have studied at least one semester of calculus =  0.47 × 0.47 = 0.2209

c) at least one has had more than one semester of calculus

The probability that both have studied at least one has had more than one semester of calculus =  (1 - (0.8×0.8)) = 1 - 0.64 = 0.36