Q1. A group of five applicants for a pair of identical jobs consists of three men and two women. The employer is to select two of the five applicants for the jobs. Let S denote the set of all possible outcomes for the employer's selection. Let A denote the subset of outcomes corresponding to the selection of two men and B the subset corresponding to the selection of at least one woman. List the outcomes in A, B, AUB, AN B, and An B. (Denote the different men and women by M₁, M2, M3 and W₁, W2, respectively.) Q2. Suppose two dice are tossed and the numbers on the upper faces are observed. Let S denote the set of all possible pairs that can be observed. [These pairs can be listed, for example, by letting (2, 3) denote that a 2 was observed on the first die and a 3 on the second.] (a) Define the following subsets of S: A: The number on the second die is even. B: The sum of the two numbers is even. C: At least one number in the pair is odd. (b) List the points in A, C, An B, ANĒ, ĀUB, and An C. Note: Here bar represents the complement. Example A = Ac.
Q1. A group of five applicants for a pair of identical jobs consists of three men and two women. The employer is to select two of the five applicants for the jobs. Let S denote the set of all possible outcomes for the employer's selection. Let A denote the subset of outcomes corresponding to the selection of two men and B the subset corresponding to the selection of at least one woman. List the outcomes in A, B, AUB, AN B, and An B. (Denote the different men and women by M₁, M2, M3 and W₁, W2, respectively.) Q2. Suppose two dice are tossed and the numbers on the upper faces are observed. Let S denote the set of all possible pairs that can be observed. [These pairs can be listed, for example, by letting (2, 3) denote that a 2 was observed on the first die and a 3 on the second.] (a) Define the following subsets of S: A: The number on the second die is even. B: The sum of the two numbers is even. C: At least one number in the pair is odd. (b) List the points in A, C, An B, ANĒ, ĀUB, and An C. Note: Here bar represents the complement. Example A = Ac.
College Algebra (MindTap Course List)
12th Edition
ISBN:9781305652231
Author:R. David Gustafson, Jeff Hughes
Publisher:R. David Gustafson, Jeff Hughes
Chapter8: Sequences, Series, And Probability
Section8.6: Permutations And Combinations
Problem 4SC
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Transcribed Image Text:Q1. A group of five applicants for a pair of identical jobs consists of three men and two
women. The employer is to select two of the five applicants for the jobs. Let S
denote the set of all possible outcomes for the employer's selection. Let A denote
the subset of outcomes corresponding to the selection of two men and B the subset
corresponding to the selection of at least one woman. List the outcomes in A, B,
AUB, AN B, and An B. (Denote the different men and women by M₁, M2, M3
and W₁, W2, respectively.)
![Q2. Suppose two dice are tossed and the numbers on the upper faces are observed. Let
S denote the set of all possible pairs that can be observed. [These pairs can be
listed, for example, by letting (2, 3) denote that a 2 was observed on the first die
and a 3 on the second.]
(a) Define the following subsets of S:
A: The number on the second die is even.
B: The sum of the two numbers is even.
C: At least one number in the pair is odd.
(b) List the points in A, C, An B, ANĒ, ĀUB, and An C.
Note: Here bar represents the complement. Example A = Ac.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F9501007d-f9de-429a-a289-0ae462063329%2Ff494a13f-3af2-42dc-b0b5-8729b6508bf5%2Fkmauw6b_processed.png&w=3840&q=75)
Transcribed Image Text:Q2. Suppose two dice are tossed and the numbers on the upper faces are observed. Let
S denote the set of all possible pairs that can be observed. [These pairs can be
listed, for example, by letting (2, 3) denote that a 2 was observed on the first die
and a 3 on the second.]
(a) Define the following subsets of S:
A: The number on the second die is even.
B: The sum of the two numbers is even.
C: At least one number in the pair is odd.
(b) List the points in A, C, An B, ANĒ, ĀUB, and An C.
Note: Here bar represents the complement. Example A = Ac.
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