Question

marco has a bag of red, blue, and green tiles. which set of events would be considered independent? a tile is drawn and replaced, and then a second tile is drawn. a tile is drawn and removed, and then a second tile is drawn. a red or blue or green tile is drawn. two tiles are drawn at the same time.

Explanation:

To determine independent events, we recall that independent events are those where the outcome of one event does not affect the outcome of the other.

• For the first option: When a tile is drawn and replaced, the total number of tiles and the probability distribution of tile colors remain the same for the second draw. So the outcome of the first draw (and replacement) does not affect the second draw.
• For the second option: Removing a tile changes the total number of tiles and the probability of drawing each color for the second draw, so these events are dependent.
• The third option is just a single event (drawing any tile) and not a set of two events to check for independence.
• The fourth option: Drawing two tiles at the same time means the outcome of one "draw" (though simultaneous) is related to the other as they are from the same set of tiles, and the selection of one affects the other (since there's no replacement in effect here in terms of available tiles).

Answer:

A. A tile is drawn and replaced, and then a second tile is drawn.