INTRODUCTION TO
PROBABILITY
Objectives:
By the end of this session learners should be able to;• Understand the concept of sample space and events
• Learn how to calculate the probability of an event
• Understand different types of events: mutually exclusive, exhaustive
• Apply the additive rules of probability
• Explore real-world applications of probability in IT
Sample Space
• Definition: The set of all possible outcomes of a random experiment.
• Examples:
• Flipping a coin: {Heads, Tails}
• Rolling a die: {1, 2, 3, 4, 5, 6}
Events:
• Definition: A subset of the sample space. An event consists of one or
more outcomes.
• Examples:
• Rolling an even number on a die: {2, 4, 6}
• Getting a head when flipping a coin: {Heads}
Types of Events
Mutually Exclusive Events:
• Definition: Events that cannot happen at the same time.
• Example: Rolling a 2 or a 3 on a die. These events do not overlap.
Exhaustive Events:
• Definition: A set of events is exhaustive if it covers all possible
outcomes.
• Example: Rolling an even number or an odd number on a die. These
two events cover the entire sample space.
Probability of an Event:
• Definition: The measure of the likelihood that an event will occur.
Additive Rules of Probability:
• Definition: For any two mutually exclusive events A and B, the
probability that A or B will occur is the sum of their individual
probabilities.
General Additive Rule:
• Definition: For any two events A and B, the probability that A or B (or
both) will occur.
Real-World Applications in IT
• Network Reliability:
Probability used to model and predict network failures.
• Machine Learning:
Algorithms use probability to make predictions and decisions.
• Data Security:
Probability models assess the risk of data breaches and encryption success.
Summary
• Sample space
• Event
• Probability of an event
• Additive rules
• Applications
Q&A
Trial Questions