Question

A number cube is rolled two times. The first time it lands showing an even number. The second time it lands showing the number 5. Identify whether this event is independent or dependent. Explain your answer

Answer 1

The event is independent.

Explanation:

In statistics and probability, when an experiment is conducted, the outcomes of the experiment are recorded. These outcomes are known as events. The events are assigned probability according to their occurrence.

There are two types of events:

1. Independent events
2. Dependent events.

Independent events are those events that are not affected by the occurrence (or no occurrence) of other events. These events do not effect the probability of another even taking place.

For example, the events of winning a lottery and being late for work are independent or the events of taking a cab home and making dinner are also independent.

Dependent events are those events that affects the occurrence of other events. These events are related to other events. For example, the events of robbing a bank and getting caught are dependent or the events of driving a car and getting stuck in traffic are also dependent.

The experiment described in this case is, rolling a number cube (or dice) two times.

The first time the dice shows an even number.

Th second time the dice shows the number 5.

The two events are are independent.

Because the every roll of the dice is independent of the successive rolls. So if the first roll is an even number, say 4, then the next roll being an even number or not does not matters.

Thus, the event is independent.

Answer 2

Independent; the first roll of the number cube does not affect the probability of the second roll.

Explanation:

Given : A number cube is rolled two times. The first time it lands showing an even number. The second time it lands showing the number 5.

To find : Identify whether this event is independent or dependent ?

Solution :

A number cube is rolled two times.

The first time it lands showing an even number.

The second time it lands showing the number 5.

Independent events are events for which the occurrence of one event does not affect the probability of the occurrence of the other.

Dependent events are events for which the occurrence of one event affects the probability of the occurrence of the other.

They both events are independent as the first roll of the number cube does not affect the probability of the second roll.