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 two events are independent if the occurrence of one does not affect the probability of the other.

• For the first option: When a tile is drawn and replaced, the total number of tiles and the number of each color tile remain the same for the second draw. So the outcome of the first draw (and replacement) does not affect the probability of the second draw.
• For the second option: If a tile is drawn and removed, the total number of tiles and the distribution of colors change, so the first event affects the second, meaning they are dependent.
• For the third option: This is a single event (drawing a tile of any color) rather than two events to check for independence.
• For the fourth option: Drawing two tiles at the same time means the outcome of one "draw" (since they are simultaneous) affects the other, as there are fewer tiles left for the second "draw" (even though it's simultaneous, the probability of each tile being drawn is affected by the other's presence).

So the set of events where a tile is drawn and replaced, then a second tile is drawn are independent.

Answer:

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