Statistics for Maintenance Modelling: Basic Probability Concepts

# Questions on Key Concepts¤

Let event A = the failure of component 1, and event B = the failure of component 2.

## Question 1

From the following choices, can you pick which one best describes AB? Click on "Check Answer" when you've chosen.

the event that both components have failed
the event that neither component failed
the event that component 1 failed or component 2 failed
Yes, that's right. As the intersection of events A and B, AB represents both events occurring.
No, neither component failing would have been represented by AB. AB is the intersection of events A and B, and describes the outcome that both components have failed.
No, component 1 or 2 failing is the union of A and B - AB. AB is the intersection of events A and B, and describes the outcome that both components have failed.

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## Question 2

From the following choices, can you pick the notation which describes the event that component 1 does not fail and component 2 fails? Click on "Check Answer" when you've made a selection.

AB
AB
AB
Yes, that's right. The complement of event A with the intersection of event B describes the sitiuation where component 1 doesn't fail, and component 2 does.
No, AB represents the outcome that component 1 doesn't fail or that component 2 fails. However, the intersection of these two events - AB - describes the outcome that component 1 doesn't fail and component 2 does.
No, AB is the event that component 1 fails and component 2 doesn't fail. It needs to be the other way round - AB - to describe the outcome that component 1 doesn't fail and component 2 does.