Final answer:
The subject involves calculating probabilities of drawing marbles from a bag and rolling specified numbers on a die. Probabilities are calculated based on conditions such as whether items or marbles are replaced, and the composition of the sample space.
Step-by-step explanation:
The question relates to the subject of probability, specifically to calculating the probabilistic outcomes of drawing marbles or rolling dice under certain conditions.
Probability is the measure of the likelihood that an event will occur, and it is expressed as a number between 0 and 1, where 0 indicates that the event will not occur, and 1 indicates that the event will certainly occur.
For example, in a bag containing four green marbles, three red marbles, and two yellow marbles, if Mark draws two marbles without replacement, the probability that he draws a yellow marble followed by a green marble requires us to consider the probability of the first event (drawing a yellow marble) and the probability of the second event (drawing a green marble) given the first event has occurred.
Similarly, when dealing with a fair, six-sided die, calculation of probability involves determining the chance of a certain number or set of numbers being rolled out of the six possible outcomes.
In problems involving cards with different colors and numbers, we would calculate the probability of drawing a card that is both of a certain color and number by considering how many such cards exist in relation to the total number of cards.