To determine the outcomes that are in [tex]\( A \)[/tex] or [tex]\( B \)[/tex], let's first identify the elements of each set based on the given table.
Event [tex]\( A \)[/tex]: The place is a city.
From the table, the places that are cities are:
- Tokyo
- Chicago
- Miami
So, we can write:
[tex]\[ A = \{ \text{Tokyo, Chicago, Miami} \} \][/tex]
Event [tex]\( B \)[/tex]: The place is in North America.
From the table, the places that are in North America are:
- Chicago
- Miami
- Canada
- Mexico
So, we can write:
[tex]\[ B = \{ \text{Chicago, Miami, Canada, Mexico} \} \][/tex]
Now, we need to find the union of events [tex]\( A \)[/tex] and [tex]\( B \)[/tex], which includes all outcomes that are either in [tex]\( A \)[/tex] or in [tex]\( B \)[/tex].
To form the union [tex]\( A \cup B \)[/tex], we combine all distinct elements from sets [tex]\( A \)[/tex] and [tex]\( B \)[/tex]:
- From [tex]\( A \)[/tex]: Tokyo, Chicago, Miami
- From [tex]\( B \)[/tex]: Chicago, Miami, Canada, Mexico
Combining these and removing duplicates (Chicago and Miami appear in both sets), we get:
[tex]\[
A \cup B = \{ \text{Tokyo, Chicago, Miami, Canada, Mexico} \}
\][/tex]
Therefore, the outcomes that are in [tex]\( A \)[/tex] or [tex]\( B \)[/tex] are:
[tex]\[ \{ \text{Tokyo, Chicago, Miami, Canada, Mexico} \} \][/tex]
The correct answer is not option A. The correct outcomes that are in [tex]\( A \)[/tex] or [tex]\( B \)[/tex] are:
[tex]\[ \{ \text{Tokyo, Chicago, Miami, Canada, Mexico} \} \][/tex]
