Question

Two events are listed below:

A: {The home's roof is less than 10 years}
B: {The home has a security system}
Define the event :A^c ∪ BGroup of answer choices:O The home's roof is at least 10 years or it has a no security systemO The home's roof is at least 10 years and it has a security systemO The home's roof is less than 10 years or it has a security systemO The home's roof is at least 10 years or it has a security system

Answer 1

The event A^c ∪ B represents all homes with roofs that are at least 10 years or have a security system.

Step-by-step explanation:

When evaluating the union of the complement of event A and event B, which is denoted as Ac ∪ B, we are looking for all outcomes that are either in the complement of A or in B, or in both. The complement of event A, denoted as Ac, includes all outcomes not in A. In the context of the given events, this would mean the complement of event A (the home's roof is less than 10 years) includes homes with roofs that are at least 10 years. Event B is that the home has a security system. Therefore, Ac ∪ B represents all homes with roofs that are at least 10 years or have a security system (or both).

Answer 2

Option 4) The home's roof is at least 10 years or it has a security system.

Step-by-step explanation:

We are given the following events in the question:

A: The home's roof is less than 10 years}

B: The home has a security system

We have to find the interpretation of event

`A^c \cup B`

Now,
`A^c`

This represents the complement of A and consist of events other than A,

Thus,

`A^c`: The home's roof is not less than 10 years or the home's roof is greater than equal to 10 years or the home's roof is at least 10 years.

The union of two sets is a new set that contains all of the elements that are in at least one of the two sets.

`A^c \cup B`

Thus, it can be interpreted as the home's roof is at least 10 years or the home has a security system.

Option 4) The home's roof is at least 10 years or it has a security system