The probability that a new computer functions for over 10,000 hours is

Jason Watson

Jason Watson

Answered question

2021-11-17

The probability that a new computer functions for over 10,000 hours is 0.8, the probability that it functions for over 20,000 hours is 0.4 and the probability that it functions for over 30,000 hours is 0.1. If a new computer is still working after 10,000 hours, what is the probability that
i. its total life will exceed 20,000 hours;
ii. its additional life will exceed 20,000 hours?

Answer & Explanation

Louis Smith

Louis Smith

Beginner2021-11-18Added 14 answers

Given data,
The probability that a new computer functions for over 10,000 hours is 0.8.
The probability that it functions for over 20,000 hours is 0.4.
The probability that it functions for over 30,000 hours is 0.1.
Step 1
Let X be the lime line of new computer function then,
It is given that,
P(X>10000)=0.8
P(X>20000)=0.4
P(X>30000)=0.1
If the function is works after 10000 hours then,
i) The probability that its total life will exceed 20,000 hours,
P[X>20000X>10000]=P(X>20000X>10000)P(X>10000)
=P[X>20000X>10000]
=0.40.8
=0.5
Step 2
ii) The probability that its additional life will exceed 20,000 hours,
P[X>30000X>10000]=P(X>30000X>10000)P(X>10000}
=P[X>30000X>10000]
=0.10.8
=0.125

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