/2.11 The resumés of two male applicants for a college teaching position in chemistry are placed in the same fle as the resumés of two female applicants. Two po- sitions become available, and the first, at the rank of assistant professor, is filled by selecting one of the four applicants at random. The second position, at the rank of instructor, is then filled by selecting at random one of the remaining three applicants. Using the notation M2F1, for example, to denote the simple event that the first position is filled by the second male applicant and the second position is then filled by the first female applicant, (a) list the elements of a sample space S; (b) list the elements of S corresponding to event A that the position of assistant professor is filled by a male applicant; (c) list the elements of S corresponding to event B that exactly one of the two positions is filled by a male applicant; (d) list the elements of S corresponding to event C that neither position is filled by a male applicant; (e) list the elements of S corresponding to the event ANB3B (1) list the elements of S corresponding to the event AUC; (8) construct a Venn diagram to illustrate the intersec- tions and unions of the events A, B, and C.

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A:

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A: Given, n(A ∪ B) = 97 and n(A) = n(B) = 66

Q: 5 -1 2 Compute A-613 and (613)A, where A = -3 3 -7 -3 1 1 A-613 = (613)A= -1 -1 2 -3 -3 -7 -3 1 -5

A: A=5-12-33-7-311A-6I3=5-12-33-7-311-6100010001A-6I3=5-12-33-7-311-600060006A-6I3=5-6-12-33-6-7-311-6A…

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A: Please refer the attached image for complete solution.

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A: Given, n(A ∪ B) = 99 and n(A) = n(B) = 69   The objective is to find  n(A ∩ B).

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Q: 5-1 2 Compute A-613 and (613)A, where A = -3 -3 A-61₂ = 3-7 1 1 www

A:

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A: Topic - Sets We are given that n(B) = 415n(A∩B∩C) = 120n(A∩B∩Cc)=145n(Ac∩B∩C)=125

Contingency Table

A contingency table can be defined as the visual representation of the relationship between two or more categorical variables that can be evaluated and registered. It is a categorical version of the scatterplot, which is used to investigate the linear relationship between two variables. A contingency table is indeed a type of frequency distribution table that displays two variables at the same time.

Binomial Distribution

Binomial is an algebraic expression of the sum or the difference of two terms. Before knowing about binomial distribution, we must know about the binomial theorem.