Concept explainers
a.
To find: the probability that both systems function satisfactorily.
a.
Answer to Problem 59E
Explanation of Solution
Given:
The probability that either system will function satisfactorily during a flight is 0.985.
Concept Used:
Let A and B be two independent events, then
Let E be the event that both systems function satisfactorily.
Here, backup system is independent and so the working of one system doesn’t influence that of the other system.
Also, probability that either system will function satisfactorily during a flight is 0.985.
Let O denotes the event that original system function satisfactorily.
And let B denotes the event that backup system function satisfactorily.
Then,
So, the probability that both systems function satisfactorily is:
b.
To find: the probability that both systems fail.
b.
Answer to Problem 59E
Explanation of Solution
Concept Used:
Let A and B be two independent events, then
Let
Here, backup system is independent and so the working of one system doesn’t influence that of the other system.
Also, probability that either system will function satisfactorily during a flight is 0.985.
So, the probability that either system will not work =
Let
And let
Then,
So, the probability that both systems fail is:
c.
To find: the probability that both at least one system functions satisfactorily.
c.
Answer to Problem 59E
Explanation of Solution
Concept Used:
Let A and B be two independent events, then
Let A be the event that at least one system functions satisfactorily.
Event A is complement of the event
So,
From part (b),
So, the probability that at least one system functions satisfactorily:
Chapter 9 Solutions
EBK PRECALCULUS W/LIMITS
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