Question

A drawer contains 3 red paperclips, 4 green paperclips, and 5 blue paperclips. One paperclip is taken from the drawer and then replaced. Another paperclip is taken from the drawer. Explain why this is an independent or a dependent event.

a.
Independent - the first paper clip is replaced, the sample space of 12 paperclips does not change from the first event to the second event
c.
Independent - the sample space changes from the first event to the second event
b.
Dependent - the first paper clip is replaced, the sample space of 12 paperclips does not change from the first event to the second event
d.
Dependent - the sample space changes from the first event to the second event

Answer 1

a.

Independent - the first paper clip is replaced, the sample space of 12 paperclips does not change from the first event to the second event

Explanation:

Answer 2

Answer: Option 'a' is correct.

Explanation:

As we know that "Independent events are those events whose occurrence does not depend upon its consecutive events."

That means, Probability of one occurrence does not affect the probability of other occurrence.

According to question, One paperclip is taken from the drawer and then replaced. Another paperclip is taken from the drawer.

So, It is an independent event as the first paper clip is replaced, the sample space of 12 paperclips does not change from the first event to the second event.

Hence, Option 'a' is correct.