Probability of Selecting a Red Marble

A bag consists of 8 red marbles, 7 blue marbles, 6 green marbles, and 4 yellow marbles. What is the probability of selecting a red marble?

In this problem, we're dealing with the fundamental concepts of probability, a core part of the Discrete Probability section in discrete mathematics. Probability helps us assess how likely an event is to occur, and this particular problem introduces the concept using a straightforward example. We have a collection of marbles of different colors, and we're tasked with finding out how likely we are to pick a red marble at random from the bag. To solve this, you will count the total number of red marbles and divide that by the total number of marbles overall. This fraction represents the probability of selecting a red marble.

This exercise highlights basic yet crucial ideas in probability, such as the counting principle and the concept of the sample space. The sample space in this problem includes all the marbles in the bag, as we're assuming each marble is equally likely to be drawn. Understanding this problem lays the groundwork for more complex probability problems, such as those involving conditional probability or multiple events. The straightforward nature of this problem makes it an excellent introduction to the principles of discrete probability, allowing students to grasp the foundational approach before moving on to more elaborate questions like dependent events and expected values.