Question

Suppose a person is chosen at random. Use your knowledge about the world to decide whether the event that the person has brown eyes and the event that the person is married are independent or associated.

Choose the correct answer below.

a. The two events are independent because having brown eyes does not depend on being female.
b. The two events are associated because having brown eyes does not depend on being female.
c. The two events are associated because being female depends on having brown eyes.
d. The two events are independent because being female depends on having brown eyes.

Answer 1

The two events are independent.

Explanation:

Independent events are those events that are not affected by each other.

If events X and Y are independent then the occurrence of one of these two events does not depend on the other in any way.

For two independent events X and Y the joint probability is:

`P(X\cap Y)=P(X)* P (Y)`

Define X and Y as follows:

X = a person has brown eyes

Y = a person is married.

The event of a person being married does not depend on the event of the person having brown eyes.

The two events are not at all related.

Thus, the two events are independent.