Concept explainers
a.
To calculate: The probability that a defective chip is selected.
a.
Answer to Problem 42E
The probability that a defective chip is selected is
Explanation of Solution
Given information:
A table that depicts number of defective and functioning chips manufactured by 3 companies.
Formula used:
Probability of an event E is
Calculation:
Consider the provided information that a table that depicts number of defective and functioning chips manufactured by 3 companies.
Total number of chips manufactured are 1000 and number of defective chips are 66.
Let A be an event that chip is defected.
Recall that probability of an event E is
Probability that defected chip is randomly selected is,
Thus, the probability that a defective chip is selected is
b.
To calculate: The probability that defective chip came from 3-D Images Inc.
b.
Answer to Problem 42E
The probability that defective chip came from 3-D Images Inc. is
Explanation of Solution
Given information:
A table that depicts number of defective and functioning chips manufactured by 3 companies.
Formula used:
Probability of an event E is
Given an event Q, the conditional probability of event A is
Calculation:
Consider the provided information that a table that depicts number of defective and functioning chips manufactured by 3 companies.
Total number of chips manufactured are 1000 and number of defective chips are 66.
Let A be an event that chip is from 3-D Images Inc. and B be an event that chip is defected.
Recall that probability of an event E is
Probability that chip is defected,
Probability that chip is from 3-D Images Inc. and chip is defected.
Recall that given an event Q, the conditional probability of event A is
The probability that defective chip came from 3-D Images Inc.
Thus, the probability that defective chip came from 3-D Images Inc. is
c.
To calculate: The probability that a functional chip is selected.
c.
Answer to Problem 42E
The probability that a functional chip is selected is
Explanation of Solution
Given information:
A table that depicts number of defective and functioning chips manufactured by 3 companies.
Formula used:
Probability of an event E is
Calculation:
Consider the provided information that a table that depicts number of defective and functioning chips manufactured by 3 companies.
Total number of chips manufactured are 1000, number of functional chips are 934 and number of defective chips are 66.
Let A be an event that chip is functional.
Recall that probability of an event E is
Probability that functional chip is randomly selected is,
Thus, the probability that a functional chip is selected is
d.
To explain: The company that produce most reliable graphic chip.
d.
Answer to Problem 42E
The company that produce most reliable graphic chip is CyberChip Corp.
Explanation of Solution
Given information:
A table that depicts number of defective and functioning chips manufactured by 3 companies.
Consider the provided information that a table that depicts number of defective and functioning chips manufactured by 3 companies.
Total number of chips manufactured are 1000, number of functional chips are 934 and number of defective chips are 66.
Compute the ratio of defective to functioning chip for each company.
For CyberChip Corp. the ratio of defective to functioning chip is,
For 3-D Images Inc. the ratio of defective to functioning chip is,
For MegaView Designs the ratio of defective to functioning chip is,
Observe that least defective to functioning chip ratio is for CyberChip Corp. so it is the most reliable company to manufacture graphic chip.
Thus, the company that produce most reliable graphic chip is CyberChip Corp.
Chapter 13 Solutions
Advanced Mathematical Concepts: Precalculus with Applications, Student Edition
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