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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?

Respuesta :

raphealnwobi

Answer:

​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

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