The U.S. Bureau of Citizenship and Immigration Services...

The U.S. Bureau of Citizenship and Immigration Services collects and reports information about naturalized persons in Statistical Yearbook. Suppose that a naturalized person is selected at random. Define events as follows: $A=$ the person is younger than 20 years old, $B=$ the person is between 30 and 64 years old, inclusive, $C=$ the person is 50 years old or older, and $D=$ the person is older than 64 years. Determine the following events: a. (not $A$ ) b. $(B \text { or } D)$ c. $(A \& C)$ Which of the following collections of events are mutually exclusive? d. $B$ and $C$ e. $A, B,$ and $D$ f. (not $A$ ) and (not $D$ )

The U.S. Bureau of Citizenship and Immigration Services collects and reports information about naturalized persons in Statistical Yearbook. Suppose that a naturalized person is selected at random. Define events as follows:
$A=$ the person is younger than 20 years old, $B=$ the person is between 30 and 64 years old, inclusive, $C=$ the person is 50 years old or older, and $D=$ the person is older than 64 years.
Determine the following events:
a. (not $A$ )
b. $(B \text { or } D)$
c. $(A \& C)$
Which of the following collections of events are mutually exclusive?
d. $B$ and $C$
e. $A, B,$ and $D$
f. (not $A$ ) and (not $D$ )

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Key Concepts

Mutually Exclusive Events

Events are considered mutually exclusive if they cannot occur at the same time, meaning their intersection is empty. In other words, if one event occurs, it precludes the possibility of any of the other mutually exclusive events occurring during the same trial.

Intersection of Events

The intersection of two or more events consists of all outcomes that are common to all the events involved. This is associated with the 'and' operation, meaning that the intersection event only occurs if every individual event occurs simultaneously.

Complement of an Event

In probability theory, the complement of an event refers to the set of all outcomes in the sample space that are not in the event. It represents the scenario in which the event does not occur, and its probability is computed as one minus the probability of the event itself.

Union of Events

The union of two or more events is a combined event that includes all outcomes that belong to at least one of the events. In logical terms, it corresponds to the 'or' operation, meaning that if any of the events occur, the union event is considered to have occurred.

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