Page 118 - WCS - Electrical

WORKSHOP CALCULATION & SCIENCE - CITS

Probability

Probability is a fundamental concept in mathematics and statistics that quantifies the likelihood of an event
occurring. Here are key aspects of the concept of probability:
Definition

Probability is a numerical measure of the likelihood that a particular event will occur.
It is expressed as a number between O and 1, where O indicates impossibility (event will not occur) and 1
indicates certainty (event will occur).
Types of Probability

Classical Probability: Based on equally likely outcomes. For example, the probability of rolling a fair six-sided
die and getting a 3 is 1/6.
Empirical Probability: Based on observed data or experiments. For example, the probability of raining tomorrow
based on historical weather data.
Subjective Probability: Based on personal judgment or beliefs. For example, the probability of a sports team
winning a match based on a fan’s opinion.

Events and Sample Space
An event is a set of outcomes of an experiment. For example, rolling a die and getting an even number.
The sample space is the set of all possible outcomes of an experiment. For a fair six-sided die, the sample space
is {1, 2, 3, 4, 5, 6}.
Calculating Probability
The probability of an event A, denoted as P{A), is calculated as the ratio of the number of favourable outcomes to
the total number of possible outcomes.
For equally likely outcomes, the probability of an event A is given by: P{A)= Total number of outcomes Number of
favourable outcomes
Basic Probability Rules

Complement Rule: The probability of the complement of an event A (not A) is 1 minus the probability of A: P{not
A)=l-P{A)
Addition Rule: The probability of the union of two events A and Bis given

by: P{AUB )=P{A)+P(B)-P{AnB)
Multiplication Rule: The probability of the intersection of two independent
events A and B is given by: P{An B)=P{A)xP(B) for independent events.
Applications

Probability theory is widely·used in various fields such as statistics, finance, science, engineering, and gaming to
make predictions, assess risks, and make informed decisions.
Understanding probability is essential for making informed decisions, analyzing data, and predicting outcomes in
various real-world scenarios
Exercises
Find the mode 8 1 3 8 8 4 9 6 3 8
Find the mode 3 6 7 2 4 6 8 3

Find the median 5 9 10 6 8 9
Find the median 3 6 7 2 4 6 8 3

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CITS : WCS - Electrical - Exercise 9