a Does the occurrence of the first event affect the occurrence of the second event in any way?
B
b Does the occurrence of the first event affect the occurrence of the second event in any way?
A
a Independent, see solution.
B
b Dependent, see solution.
Practice makes perfect
a We want to determine whether the events are independent or dependent. Let's recall the definitions first.
Independent Events
Dependent Events
The occurrence of one event does not affect the occurrence of the other event.
The occurrence of one event does affect the occurrence of the other event.
Let's look at the two given events.
Rolling a 4 on a six-sided die.
Spinning red on a spinner.
Notice that in these two events we are using two different objects: the die and the spinner. Since they are separate and do not affect each other in any way, the events are independent.
b Now, we know that a teacher chooses students to lead three different groups. Let's illustrate this situation on a diagram. We have a group of all students and three different groups for which the teacher assigns leaders.
First, the teacher picks one student to lead the first group.
Next, another student is to be chosen to lead the second group. However, notice that we do not include the leader of the first group. Therefore, the choice of the second leader will be affected by the choice of the first leader, because the teacher chooses now from a smaller group of students.
We have a similar situation when choosing the third leader. We cannot choose either of the students that were already chosen, so now we are choosing from the group of students with those two students excluded.
Since the occurrence of each event affects the occurrence of the other events, these three events are dependent.
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