In a large Intro Stats lecture hall, the professorreports that 55% of the studen

Question

  In a large Intro Stats lecture hall, the professorreports that 55% of the students enrolled have never taken a Calccourse, 32% have taken only one semester of Calc, and the rest havetaken two or more semesters of Calc. The professor randomly assignsstudents to groups of three to work on a project for the course.What is the probability that, of your toher two groupmates, a) neither has studied Calc? b) both have studied at least one semester of Calc? c) at least one has had more than one semester of Calc?   In a large Intro Stats lecture hall, the professorreports that 55% of the students enrolled have never taken a Calccourse, 32% have taken only one semester of Calc, and the rest havetaken two or more semesters of Calc. The professor randomly assignsstudents to groups of three to work on a project for the course.What is the probability that, of your toher two groupmates, a) neither has studied Calc? b) both have studied at least one semester of Calc? c) at least one has had more than one semester of Calc?

Explanation / Answer

a)The probability that neither has studied calc is.552=.3025, or about 30% b)The probability that both have studied at least 1 semesterof calc is just 1-a) (1-.3025=.6975), or about 70% c)P(A or B having taken 2 or more semesters of calc)=P(firstperson has taken more than 1 course)+P(second person has taken morethan 1 course)-P(both have taken at least 1course)=2(.13)-.132=.2431, or about 24% c)P(A or B having taken 2 or more semesters of calc)=P(firstperson has taken more than 1 course)+P(second person has taken morethan 1 course)-P(both have taken at least 1course)=2(.13)-.132=.2431, or about 24%

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