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 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 c. independent - the sample space changes from the first event to the second event d. dependent - the sample space changes from the first event to the second event please select the best answer from the choices provided

Explanation:

Independent events are events where the outcome of one event does not affect the outcome of the other. Here, since the first paper - clip is replaced, the total number of paper - clips (\(3 + 4+5=12\)) remains the same for both draws. The probability of drawing a particular color paper - clip in the second draw is not affected by the result of the first draw. In dependent events, the sample space changes (e.g., if the first paper - clip was not replaced). But in this case, replacement means the sample space (\(n = 12\)) is unchanged for both events, so the events are independent.

Answer:

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