Final answer:
The question asks about the probabilities of specific outcomes when drawing items from a bag without replacement, which involves calculating the chances of drawing certain colors of blocks or marbles consecutively, considering the changing contents of the bag after each draw.
Step-by-step explanation:
The question involves determining the probability of certain outcomes when drawing blocks or marbles from a bag without replacement. To find the desired probabilities, one must consider the total number of possible outcomes and the number of outcomes that favor the desired event. The principle of drawing without replacement is crucial since the probabilities change after each draw due to the reduction in total items.
For example, if a bag contains four blue and three white marbles, the probability of drawing a blue marble first is 4/7. If the marble isn't replaced, the contents of the bag change for the second draw. Hence, if a blue marble is drawn first and set aside, the probability of drawing a blue marble a second time becomes 3/6 or 1/2.
When calculating combined probabilities of consecutive events without replacement, it's important to multiply the probability of the first event by the probability of the second event, given the first event has occurred. For instance, if the question was to find the probability of drawing a blue and then a white marble, one would calculate it as (4/7) * (3/6) after the first blue marble is drawn and set aside.