Introduction

Understanding the fundamental concepts of probability is essential for making informed decisions in various fields, from business to science. In this chapter, we will delve into the concepts of events and event space, building the foundation for a deeper exploration of probability theory.

Events and Event Space

An event in probability refers to a specific outcome or set of outcomes that we are interested in observing or analyzing. It could be as simple as flipping a coin and observing whether it lands on heads or tails. Event space, on the other hand, encompasses all possible outcomes of an experiment. In the coin-flipping scenario, the event space includes both heads and tails.

Examples: Let’s consider a few examples to clarify these concepts.

• Imagine rolling a six-sided die. The event “rolling an even number” includes the outcomes 2, 4, and 6. The event space, in this case, is {1, 2, 3, 4, 5, 6}.

• In a deck of playing cards, drawing a red card is an event. The event space includes all 52 cards, and the event “drawing a red card” consists of hearts and diamonds.

Independent and Mutually Exclusive Events

An important distinction to make is between independent and mutually exclusive events. Independent events are those where the occurrence of one event does not affect the probability of the other event occurring. For example, rolling a die and flipping a coin are independent events.

On the other hand, mutually exclusive events are events that cannot occur simultaneously. For instance, in the roll of a die, the events “rolling a 2” and “rolling a 4” are mutually exclusive since they cannot happen together.