Random Experiment Example

Random Experiment Example

1. Give an example of an event in a random experiment and define its complement.

APA

In a random experiment, an example of an event could be rolling a six-sided die and getting an even number. The possible even outcomes when rolling the die are 2, 4, and 6.

Event

Let $A$ be the event of rolling an even number:
$A=\{2,4,6\}$

Complement of the Event

The complement of event $A$, denoted as A′A’A′ or AcA^cAc, includes all outcomes that are not part of event $A$. In this case, the complement would be rolling an odd number, which corresponds to the outcomes 1, 3, and 5.

Complement Definition

The complement of event $A$ is defined as:
A′={1,3,5}A’ = \{1, 3, 5\}A′={1,3,5}…

In a random experiment, an example of an event could be rolling a six-sided die and getting an even number. The possible even outcomes when rolling the die are 2, 4, and 6.

Event

Let $A$ be the event of rolling an even number:
$A=\{2,4,6\}$

Complement of the Event

The complement of event $A$, denoted as A′A’A′ or AcA^cAc, includes all outcomes that are not part of event $A$. In this case, the complement would be rolling an odd number, which corresponds to the outcomes 1, 3, and 5.

Complement Definition

The complement of event $A$ is defined as:
A′={1,3,5}A’ = \{1, 3, 5\}A′={1,3,5}…

In a random experiment, an example of an event could be rolling a six-sided die and getting an even number. The possible even outcomes when rolling the die are 2, 4, and 6.

Event

Let $A$ be the event of rolling an even number:
$A=\{2,4,6\}$

Complement of the Event

The complement of event $A$, denoted as A′A’A′ or AcA^cAc, includes all outcomes that are not part of event $A$. In this case, the complement would be rolling an odd number, which corresponds to the outcomes 1, 3, and 5.

Complement Definition

The complement of event $A$ is defined as:
A′={1,3,5}A’ = \{1, 3, 5\}A′={1,3,5}…