a.
Find the probability that all the three components
a.
Answer to Problem 84E
The probability that all the three components functions properly is 0.7448.
Explanation of Solution
Given info:
The information is based on purchasing the audio components like a receiver, pair of speakers and a CD player. Here A1 be the
Calculation:
Define the event as given below:
Mutually independent events:
Two or more events are said to be mutually independent, if the occurrence of one does not affect the occurrence of other. Events
The probability that all the three components functions properly can be obtained as
Thus, the probability of an event
b.
Find the probability that at least one of the three components needs service.
b.
Answer to Problem 84E
The probability that at least one of the three components needs service is 0.2552.
Explanation of Solution
Calculation:
The probability that at least one of the three components needs service is obtained as:
From previous part (a),
The probability of event
Thus, the probability of an event
c.
Find the probability that all the three components need service.
c.
Answer to Problem 84E
The probability that all the three components need service is 0.0002.
Explanation of Solution
Calculation:
The probability that at least one of the three components needs service is obtained as:
The probability of the event
Thus, the probability of an event
d.
Find the probability that only receiver needs service.
d.
Answer to Problem 84E
The probability that only receiver needs service is 0.0392.
Explanation of Solution
Calculation:
The probability that only receiver needs to be serviced can be obtained as
Thus, the probability that only receiver needs service is 0.0392.
e.
Find the probability that exactly one of the three components needs to be serviced.
e.
Answer to Problem 84E
The probability that exactly one of the three components needs to be serviced is 0.2406.
Explanation of Solution
Calculation:
The probability that exactly one of the three components needs to be serviced is obtained as:
The probability of the event
Thus, the probability of an event
f.
Find the probability that all the three components functions properly that at least one of the components fails within a month after the warranty.
f.
Answer to Problem 84E
The probability that the happening of the event that fails with a month after the warranty is zero.
Explanation of Solution
Justification:
There is no chance that the component fails with in the month after the warranty.
Thus, the probability for the occurrence of such event is zero.
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Chapter 2 Solutions
EBK PROBABILITY AND STATISTICS FOR ENGI
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