Question

for the given pair of events, classify the two events as independent or dependent.

finding your portable cd player works
finding your bathroom light works

choose the correct answer below.

a. the two events are independent because the occurrence of one does not affect the probability of the occurrence of the other.
b. the two events are independent because the occurrence of one affects the probability of the occurrence of the other.
c. the two events are dependent because the occurrence of one affects the probability of the occurrence of the other.
d. the two events are dependent because the occurrence of one does not affect the probability of the occurrence of the other.

Explanation:

Define the relationship between the events

Using the Independent Events Probability and Dependent Events knowledge points

Two events are independent if the occurrence of one event does not affect the probability of the occurrence of the other event. Conversely, they are dependent if the occurrence of one event affects the probability of the occurrence of the other.

Analyze the given events

Using the Independent Events Probability knowledge point

The two events are:

1. Finding your portable CD player works.
2. Finding your bathroom light works.

A portable CD player runs on its own batteries or separate power source, while a bathroom light is connected to the household electrical grid. The operational status of a portable CD player has no physical or logical connection to the operational status of a household bathroom light. Therefore, knowing that one of these devices works does not change the probability that the other device works.

Select the correct option

Using the Independent Events Probability knowledge point

Since the occurrence of one event does not affect the probability of the occurrence of the other, the events are independent. This matches option A.

Answer:

• A. The two events are independent because the occurrence of one does not affect the probability of the occurrence of the other. (Correct answer)
• B. The two events are independent because the occurrence of one affects the probability of the occurrence of the other.
• C. The two events are dependent because the occurrence of one affects the probability of the occurrence of the other.
• D. The two events are dependent because the occurrence of one does not affect the probability of the occurrence of the other.