A digital scale that provides weights to the nearest gram

Chapter 2, Problem 21E

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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)

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,...}.


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