Concept explainers
Factory Output A manufacturing company has three factories: X, Y, and Z. The daily output of each is shown here.
If 1 item is selected at random, find these
a. It was manufactured at factory X or is a stereo.
b. It was manufactured at factory Y or factory Z.
c. It is a TV or was manufactured at factory Z.
a.
The probability of selecting an item produced by factory X or it is a stereo.
Answer to Problem 4.3.16RE
The probability of selecting an item produced by factory X or it is a stereo is 0.548.
Explanation of Solution
Given info:
A company has three manufacturing units X, Y and Z. The three units produce televisions and stereos.
Calculation:
Let A be the event of selecting an item manufactured by unit X.
The probability of any event A is given below:
Thus, the probability of selecting an item manufactured by unit X is 0.231.
Let B be the event of selecting a stereo.
The probability of any event B is given below:
Thus, the probability of selecting a stereo is 0.375.
Addition rule for dependent events:
If two events A and B are said to be dependent, then the addition of events A and B is,
The number of items common between unit X and stereo is 6.
The probability of selecting an item produced by unit X or it is a stereo is given below,
Thus, the probability of selecting an item produced by unit X or it is a stereo is 0.548.
b.
The probability of selecting an item produced by unit Y or by unit Z.
Answer to Problem 4.3.16RE
The probability of selecting anitem produced by unit X or by unit Y is 0.77.
Explanation of Solution
Calculation:
Let C be the event of selecting an item manufactured by unit Y.
The probability of any event C is given below:
The probability of selecting an item manufactured by unit Y is given below:
Thus, the probability of selecting an item manufactured by unit Y is 0.5.
Let D be the event of selecting an item manufactured by unit Z.
Thus, the probability of selecting an item manufactured by unit Z is 0.27.
Addition rule for independent events:
If two events A and B are said to be independent, then the addition of events A and B is,
The probability of selecting an item produced by unit Y or by unit Z is given below,
Thus, the probability of selecting an item produced by unit Y or by unit Z is 0.77.
c.
The probability of selecting a TV or a unit produced by unit Z.
Answer to Problem 4.3.16RE
The probability of selecting a TV or a unit produced by unit Z is0.769.
Explanation of Solution
Calculation:
Let E denote the event of selecting a TV.
The probability of any event E is given below:
Thus, the probability of selecting a TV is 0.625.
The number of items common between TV and unit Z is 15.
The probability of selecting a TV or a unit produced by unit Z is given below:
Thus, the probability of selecting a TV or a unit produced by unit Z is 0.769.
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Chapter 4 Solutions
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