Final answer:
The question pertains to the subject of probability within Mathematics, focusing on events that are dependent due to the non-replacement of marbles in a selection process. It illustrates how the probability of subsequent draws changes as the composition of the bag is altered through the removal of marbles.
Step-by-step explanation:
The subject of the question is probability which falls under Mathematics, specifically combinatorics and probability theory. The grade level is likely High School, as this type of probability question is commonly addressed at that educational stage. The question revolves around the scenario of selecting marbles from a bag without replacement, which affects the probabilities of subsequent draws.
Example Explanation
In the provided examples, we have different scenarios where marbles are drawn from a bag, either with or without replacement, affecting the probability of drawing a marble of a certain color. When James replaces the marble after drawing, the probability of drawing a blue marble remains the same for the second draw because the composition of the bag is unchanged. This illustrates the concept of independent events in probability.
Conversely, when Maria or Mark draw marbles without replacing them, the number of marbles in the bag changes, which impacts the probabilities of subsequent draws. This is an example of dependent events, as the outcome of the second draw is influenced by the first. The problem points out how removing marbles from the bag without replacement adjusts the odds of the next draw.