Final answer:
The student's question involves calculating conditional probability, which determines the likelihood of one event given that another event has occurred. An example given illustrates how to calculate this by adjusting the sample space after the first event has occurred.
Step-by-step explanation:
The question you've asked pertains to the concept of conditional probability, which is a measure of the probability of an event occurring given that another event has already occurred. To calculate this, we generally use the formula P(A|B) = P(A and B)/P(B), where P(A|B) is the probability of event A occurring given event B has occurred, P(A and B) is the joint probability of both events occurring, and P(B) is the probability of event B occurring.
Let's consider an example similar to one of the examples you've listed: Suppose a bag contains 5 red marbles and 5 blue marbles. If a marble is drawn from the bag at random and it's blue, what is the probability that another marble drawn at random is also blue? To find the conditional probability that the second marble is blue given that the first marble is blue, we restrict our sample space to the scenario where the first marble is blue. The new sample space has only 9 marbles because one blue marble is already drawn, leaving us with 4 blue and 5 red marbles. The probability that the second marble is blue is therefore 4/9.