Solution Found!
A digital scale that provides weights to the nearest gram
Chapter 2, Problem 21E(choose chapter or problem)
A digital scale that provides weights to the nearest gram is used.
(a) What is the sample space for this experiment? Let denote the event that a weight exceeds 11 grams, let denote the event that a weight is less than or equal to 15 grams, and let denote the event that a weight is greater than or equal to 8 grams and less than 12 grams. Describe the following events.
(b) \(A \cup B\)
(c) \(A \cap B\)
(d) \(A^{\prime}\)
(e) \(A \cup B \cup C\)
(f) \((A \cup C)^{\prime}\)
(g) \(A \cap B \cap C\)
(h) \(B^{\prime} \cap C\)
(i) \(A \cup(B \cap C)\)
Equation transcription:
Text transcription:
A cup B
A cap B
A^{prime}
A cup B cup C
(A cup C)
(A cup C)^{prime}
A cap B cap C
B^{prime} cap C
A cup(B cap C)
Questions & Answers
QUESTION:
A digital scale that provides weights to the nearest gram is used.
(a) What is the sample space for this experiment? Let denote the event that a weight exceeds 11 grams, let denote the event that a weight is less than or equal to 15 grams, and let denote the event that a weight is greater than or equal to 8 grams and less than 12 grams. Describe the following events.
(b) \(A \cup B\)
(c) \(A \cap B\)
(d) \(A^{\prime}\)
(e) \(A \cup B \cup C\)
(f) \((A \cup C)^{\prime}\)
(g) \(A \cap B \cap C\)
(h) \(B^{\prime} \cap C\)
(i) \(A \cup(B \cap C)\)
Equation transcription:
Text transcription:
A cup B
A cap B
A^{prime}
A cup B cup C
(A cup C)
(A cup C)^{prime}
A cap B cap C
B^{prime} cap C
A cup(B cap C)
ANSWER:Solution :
Step 1 of 9:
Given a digital scale that provides weight to the nearest gram is used.
Our goal is:
a). We need to find what is the sample space for this experiment.
b). .
c). .
d). .
e). .
f). .
g). .
h). .
i). .
a). Now we have to find what is the sample space for this experiment.
Let A, B, and C be the three events.
A is a weight exceeds 11 grams.
B is a weight is less than or equal to 15 grams and
C is a weight is greater than or equal to 8 grams and less than 12 grams.
The nonnegative integers from 0 to the largest integer that can be displayed by the scale is S.
We consider X is the weight.
We know A, B, and C be the three events.
So A is X>11, B is X15, C is 8X < 12.
Then S = {0, 1, 2,...}.