A regional telephone company operates 3 identical relay stations at different locations. During a period of one year, the number of malfunctions reported by each station and the causes are shown below. Station A B C Problems with electricity supply 2 1 1 Computer crash 4 3 2 Electrical equipment failures 5 4 2 Failures caused by human errors 7 7 5 Where events are defined as: *Event A -> Failure at station A *Event B -> Failure at station B *Event C -> Failure at station C *Event D -> Electricity supply failure *Event E -> Computer crash failure *Event F -> Failure in electrical equipment *Event G -> Failure due to human errors a) What is the probability of a failure of station C? b) What is the probability of a failure due to human error? c) What is the probability of a computer crash and it happens at station B? d) What is the probability of failure of the electrical equipment or station A? e) Suppose you report a failure and it is found to have been caused by other human errors, what is the probability that it came from station C?
A regional telephone company operates 3 identical relay stations at different locations. During a period of one year, the number of malfunctions reported by each station and the causes are shown below.
| Station | A | B | C |
| Problems with electricity supply | 2 | 1 | 1 |
| Computer crash | 4 | 3 | 2 |
| Electrical equipment failures | 5 | 4 | 2 |
| Failures caused by human errors | 7 | 7 | 5 |
Where events are defined as:
*
*Event B -> Failure at station B
*Event C -> Failure at station C
*Event D -> Electricity supply failure
*Event E -> Computer crash failure
*Event F -> Failure in electrical equipment
*Event G -> Failure due to human errors
a) What is the probability of a failure of station C?
b) What is the probability of a failure due to human error?
c) What is the probability of a computer crash and it happens at station B?
d) What is the probability of failure of the electrical equipment or station A?
e) Suppose you report a failure and it is found to have been caused by other human errors, what is the probability that it came from station C?
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