2. Some terminologies
Experimental Probability
- is the other type of probability, which is based on
experiments frequency of an
outcome/number of trials.
- it is the ratio of the number of times an outcome occured
to the total of events or trials.
experimental probability = frequency of an outcome/total
number of trials.
Theoretical Probability - mathematically determined.
Simulation - is the process of finding the experimental
probability
Empirical Study - performing experiment repeatedly,
collect, and combine the data and analyzing the results.
Probability Histogram - a bar chart used for data
involving probabilities
3. 1. Counting
Arrangements/Outcomes
one way to count the number of
possible outcomes graphically is
tree diagram.
the list of all possible outcomes
is called the sample space.
event - a collection of one or
more outcomes in the sample
space
4. COUNTING ARRANGEMENTS = HOW MANY
ARRANGEMENTS? USE FACTORIAL
FACTORIAL - is the product of all positive integers
from n counting backwards to 1, denoted by n!.
Example: find 5!
5! means 5 x 4 x 3 x 2 x 1
5! = 5 x 4 x 3 x 2 x 1
5! = 120
SAMPLE PROBLEM:
How many ways can you arrange your 10 books in
a shelf?
Answer: USE FACTORIAL 10! = 3,628,800
5. 2. THE FUNDAMENTAL PRINCIPLE
OF COUNTING
Fundamental Principle of Counting says that:
“If event M can occur in m ways and is followed by an
event N that can occur in n ways, then the event M
followed by event N can occur in n times m ways.”
EXAMPLE, A and B are two events. To know how many
ways A and B can occur, multiply the number of ways
for A by the ways for B.
SAMPLE PROBLEM: If a restaurant offers 10 different
types of burgers, 5 different types of pizza, and 3
different beverages, how many combinations/meals
can you pick?
ANSWER: use FPC!
Let x = number of meals
M = 10 x 5 x 3
M = 150
Then, you can choose from 150 meals.
6. 3. PERMUTATION AND
COMBINATION
PERMUTATION - arrangement or listing of
numbers in which the order does matter
FORMULA: nPr = n! / (n-r)!
where n = total number of possible outcomes
r = number of items taken at a time
COMBINATION - arrangement or listing of numbers
in which the order does not matter
FORMULA: nCr = n! / (n-r)!r!
where n = total number of possible outcomes
r = number of items taken at a time
7. 4. some types of events
1) simple event - a single event
2) compound event - two or more simple events
3) independent event - two or more events
wherein one event do not affect other event's
outcome
4) dependent event - two or more events wherein
one event affect the other's outcome
5) mutually exclusive event - two events wherein
one event cannot happen with the second event
at the same time
6) inclusive events - two events in which one
event can happen at the same time with the
8. 5. finding the probabilities.
THE PROBABILITY OF INDEPENDENT EVENT
- if two events are independent, then the
probability of both A and B to occur is the product
of the individual probabilities of the two events.
P(A and B) = P(A) times P(B)
THE PROBABILITY OF DEPENDENT EVENT
- if two events are dependent, then the probability
of both A and B to occur is the product of the
probability of A and the probability of B after the
event A.
P(A and B) [dependent] = P(A) times P(B after
A)
9. THE PROBABILITY OF MUTUALLY EXCLUSIVE
EVENTS
- if two events are mutually exclusive events, then
the probability that both A or B to occur is the sum of
the probabilities of A and B.
P(A or B) = P(A) + P(B)
THE PROBABILITY OF INCLUSIVE EVENTS
- if two events are inclusive events, then the
probability for both A or B to occur is the sum of the
probabilities of A and B decreased by the probability
of both A and B to occur.
P(A or B) = P(A) + P(B) - P(A and B)
