Final answer:
The subject revolves around calculating probabilities in different contexts, such as drawing marbles from a bag or playing a slot machine, and understanding the effects of drawing with or without replacement.
Step-by-step explanation:
The question relates to the subject of probability and how to calculate it in different scenarios involving randomness. Given the various contexts in these problems, such as drawing marbles from a bag or playing a slot machine, the key concept is to determine the likelihood of specific outcomes, like getting a marble of a certain color or winning money from the slot machine.
Example of Calculating Probability:
For example, if a bag contains four blue and three white marbles, and a marble is drawn at random, the probability of drawing a blue marble (P(B)) is calculated by dividing the number of blue marbles by the total number of marbles:
P(B) = Number of blue marbles / Total number of marbles
In this case, P(B) = 4 / (4 + 3) = 4 / 7.
If the procedure involves drawing without replacement, the total number of marbles in the bag changes after each draw, affecting subsequent probabilities. If replacement occurs, the probabilities remain constant because the composition of the bag does not change after each draw.