Question

1. A study randomly assigned students attending a large college to different professors for Calculus 1, with equal numbers of students assigned to each professor. The experienced professors were Peters, Parker, and Nguyen. The inexperienced professors were Diaz and Black. The researchers of this study reported students who had experienced teachers for Calculus 1 did better in Calculus 2.

1. List the equally likely outcomes that could occur for assignment on one student to a professor
2. Suppose the event of interest, event A, is that a teacher is experienced. List the outcomes that make up event A.
3. What is the probability a student will be assigned to an experienced teacher?
4. List the outcomes in the complement of event A.
5. List the probability a student will be assigned to an inexperienced teacher.

Answer 1

Answer :-

The probability of an event A is the ratio of favorable number of outcomes related to the event A and the number of mutually exclusive , mutually exhaustive and equally likely all possible outcomes.

                    This can be denoted as P( A )

A study looked at the way strudents attending the large college were randomly assigned ti different proffesors for calculus 1. the list of proffesors is given.There are total 5 proffesors.Among them Diaz and black are inexperienced proffesors.other are experienced proffesors. The names of the proffesors are listed below..

S.No	NAME
1	Peters
2	parker
3	Diaz
4	nguyen
5	Black

The selection of proffesors is equally likely.

(a) The number of all possible outcomes (n) = 5. Assuming all the possible outcomes is equally likely.

The equally likely all possible outcomes that could occur is (peters , Parker , Diaz , Nguyen , Black )

(b) suppose , the event of interest (A) is that the the teacher is experienced.the number of outcomes favorable to the event A is = 3

The outcomes favorable to the event A that could occur is (Peters , parker , Nguyen )

(c) In this case , number of outcomes favorable to the event A is =3

Then , the probability that one student will be assigned to an experianced teacher is defined as ,

Substituting the values in their respective positions , we have

Thus , the probability thet one student will be assigned to an experianced teacher is 0.6

(d) the complement event of interest A is that the teacher is inexperienced. the number of outcomes favorable to the complement event A = 2

the outcomes favorable to the complement of event A that could occur is (diaz , Black)

(e) in this case , number of outcomes indicating that the teacher is inexperienced

Then , the probability that one student will be assigned to an inexperienced teacher is defined as ,

substituting their values in their respective positions , we have

Thus , the probability that one student will be assigned to an inexperienced teacher is 0.4

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