Find-the-Probability_20240516_090646_0000.pdf

probability

1. FIND THEFIND THE
PROBABILITY OFPROBABILITY OF
(A∪(A∪BB))
Presented by: Group 2

2. Probability is simply how likely something is
to happen. Whenever we're unsure about the
outcome of an event, we can talk about the
probabilities of certain outcomes—how likely
they are.
probabilityprobability

3. In probability theory, the union of two events
refers to the event that at least one of the two
events occurs.
union of two events in probabilityunion of two events in probability
theorytheory

4. union of two events in probabilityunion of two events in probability
theorytheory
The union of events can be visualized using
Venn diagrams, where the entire sample
space is represented by a rectangle, and the
events A and B are represented by circles
within this rectangle.

5. Define the notationDefine the notation
for the union offor the union of
two events (A U B).two events (A U B).

6. Define the notation for the union ofDefine the notation for the union of
two events (A U B).two events (A U B).
In the field of probability and statistics, the
union of two events is a fundamental
concept that plays a crucial role in various
mathematical calculations.

7. Define the notation for the union ofDefine the notation for the union of
two events (A U B).two events (A U B).
The notation for the union of two events is represented
by the symbol "∪". Mathematically, the union of two
events can be expressed as:
A U B = {x | x ∈ A or x ∈ B}

8. Define the notation for the unionDefine the notation for the union
of two events (A U B).of two events (A U B).
This notation signifies that the union of events A
and B involves all elements 'x' such that 'x'
belongs to event A or 'x' belongs to event B. This
representation highlights that the union of two
events is a comprehensive event that aggregates
all possible outcomes from both original events.

9. Define the notation for the union ofDefine the notation for the union of
two events (A U B).two events (A U B).
Understanding the notation for the union of two
events is essential in various probability and
statistics calculations. For instance, when
calculating the probability of the union of two
events, the notation A U B is used to indicate
the event where either event A, event B, or
both events can occur.

10. non- mutually and mutually exclusivenon- mutually and mutually exclusive
eventsevents
Mutually exclusive events
are events in probability
theory that cannot occur
simultaneously. If one
event occurs, the other
cannot occur.
Non-mutually exclusive
events are events that
can occur at the same
time. They have one or
more outcomes in
common.

11. how it affects the probability of theirhow it affects the probability of their
unionunion
Mutually exclusive events affect the probability of
their union in a straightforward manner. When two
events are mutually exclusive, it means that if one
event occurs, the other cannot occur simultaneously.
The probability of the union of two mutually
exclusive events is simply the sum of their individual
probabilities.

12. EXAMPLESEXAMPLES

13. examplesexamples
1.In the experiment of rolling a single die, find the
union of the events E: "the number rolled is even"
and T : "the number rolled is greater than two".
2. A scenario where we want to find the probability
of the union of two events: flipping a fair coin and
getting either heads or tails.

14. SUMMARYSUMMARY
Key points:
The union of two events in probability theory indicates that at least one of
the two events occurs.
Denoted as A ∪ B, it encompasses outcomes from either event A, event B,
or both.
Visualized using Venn diagrams, where events A and B are represented by
circles within a rectangle representing the sample space.
This notation signifies that the union of events A and B includes all
elements 'x' belonging to either A or B.
Mutually exclusive events cannot occur simultaneously.
Probability of the union of two mutually exclusive events is the sum of their
individual probabilities.

15. SUMMARYSUMMARY
Understanding the probability of event
unions is essential for informed decision-
making and risk assessment. Mastery of
this concept forms the basis for
advanced probabilistic analyses and
facilitates accurate statistical inference
from observed data.

16. Thank you for your attention and
engagement throughout this
presentation!