Concept explainers
Quality control: A population of 600 semiconductor wafers contains wafers from three lots. The wafers are categorized by lot and by whether they conform to a thickness specification: with die results shown in the following table. A wafer is chosen at random from the population.
What is the
What is the probability that a wafer is conforming?
What is the probability that a wafer is from Lot A and is conforming?
Given that the wafer is from Lot A, what is the probability that it is conforming?
Given that the wafer is conforming, what is the probability that it is from Lot A?
Let
(a)
The probability that randomly chosen wafer belongs to Lot A.
Answer to Problem 42E
Explanation of Solution
Given:
The following table categorizes 600 wafer.
Lot | Conforming | Non Conforming |
A | 88 | 12 |
B | 165 | 35 |
C | 260 | 40 |
Formula Used:
Probability of an event is given by
Calculation:
Let
Hence, the probability of the event that randomly chosen wafer belongs to Lot A,is
(b)
The probability that randomly chosen wafer is conforming.
Answer to Problem 42E
Explanation of Solution
Given:
The following table categorizes 600 wafer.
Lot | Conforming | Non Conforming |
A | 88 | 12 |
B | 165 | 35 |
C | 260 | 40 |
Formula Used:
Probability of an event is given by
Calculation:
Let
Hence, the probability of the event that randomly chosen wafer is conforming, is
(c)
The probability that the wafer is from Lot A and conforming.
Answer to Problem 42E
Explanation of Solution
Given:
The following table categorizes 600 wafer.
Lot | Conforming | Non Conforming |
A | 88 | 12 |
B | 165 | 35 |
C | 260 | 40 |
Formula Used:
For any two t events
Calculation:
Let
Let
So,
There are 88wafer from Lot A who are conforming.
The probability that the wafer is from Lot A and conforming, is
(d)
The probability of conforming wafer, given wafer belongs toLot A.
Answer to Problem 42E
Explanation of Solution
Given:
The following table categorizes 600 wafer.
Lot | Conforming | Non Conforming |
A | 88 | 12 |
B | 165 | 35 |
C | 260 | 40 |
Formula Used:
For any two dependent events
Where
Calculation:
Let
Let
So,
There are 88 wafer from Lot A who are conforming.
Therefore,
So, the probability of the event “conforming wafer, given wafer belongs to Lot A” is calculated as follows:
The probability of conforming wafer, given wafer belongs to Lot A, is
(e)
The probability to a waferbelongs to Lot A, given that wafer is conforming.
Answer to Problem 42E
Explanation of Solution
Given:
The following table categorizes 600 wafer.
Lot | Conforming | Non Conforming |
A | 88 | 12 |
B | 165 | 35 |
C | 260 | 40 |
Formula Used:
For any two dependent events
Where
Calculation:
Let
Let
So,
There are 88 wafer from Lot A who are conforming.
Therefore,
So, the probability of the event “a wafer belongs to Lot A, given that wafer is conforming” is calculated as follows:
The probability to a wafer belongs to Lot A, given that wafer is conforming, is
(f)
To explain: Whether the events
Answer to Problem 42E
No, the events
Explanation of Solution
Given:
The following table categorizes 600 wafer.
Lot | Conforming | Non Conforming |
A | 88 | 12 |
B | 165 | 35 |
C | 260 | 40 |
Formula Used:
For any two independent events
Calculation:
Let
Let
So,
There are 88 wafer from Lot A who are conforming.
Now
Therefore, the two events
Hence, the events
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Chapter 5 Solutions
Elementary Statistics 2nd Edition
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