Question

Quincy chooses a colored marble from a mixed bag and writes down the color. Quincy leaves it out and then draws another. Are these two events dependent or independent?

Answer 1

Quincy's action of drawing a marble and not replacing it leads to dependent events as the outcome of the first draw affects the probability of the second draw.

Step-by-step explanation:

When Quincy draws a marble from the bag, records its color, and sets it aside, the draw affects the composition of the marbles remaining in the bag. Therefore, these two events are dependent. If the first marble had been replaced, the events would have been independent, as replacing the marble keeps the composition of the bag the same after each draw, thus not affecting the probabilities of drawing any specific color the second time (just like in James's example). Since the first marble is not replaced, the probability of drawing a marble of a specific color on the second draw will be different based on the outcome of the first draw, making the events dependent.