stats projects in a large introductory statistics lecture hall, the professor reports that 55% of the students enrolled have never taken a calculus course, 32% 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. what is the probability that the first groupmate you meet has studied a) two or more semesters of calculus? b) some calculus? c) no more than one semester of calculus? de veaux, richard d.; velleman, paul f.; bock, david e.. intro stats (p. 405). pearson education. kindle edition.

Calculating the likelihood of experiments happening is one of the branches of mathematics known as probability. We can determine everything from the likelihood of receiving heads or tails when tossing a coin to the likelihood of making a research blunder, for instance, using a probability. It is crucial to grasp this branch's most fundamental concepts in order to fully comprehend it, including the formula for computing probabilities in equiprobable sample spaces, the likelihood of two events joining together, the probability of the complementary event, etc.

In the given question, we have:

55% = 0.55 of the students enrolled have never taken a calculus course,

32% = 0.32 have taken only one semester of calculus,

and

13% = 0.13 have taken two or more semesters of calculus.

So,

(a) Probability of two or more semesters of calculus

= 1 - [P(0) + P(1)]

= 1 - (0.55 + 0.32)

= 1 - 0.87

= 0.13

(b) The Probability of some calculus

= 1 - P(No calculus)

= 1 - 0.55

= 0.45

(c) The Probability of no more than one semester of calculus

= P(0) + P(1)

= 0.55 + 0.32

= 0.87.

Hence,

a) The Probability of two or more semesters of calculus is 0.13

b) The Probability of some calculus is 0.45

c) The Probability of no more than one semester of calculus is 0.87.

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