Probability is a branch of mathematics that deals with describing how likely events are to occur. An experiment is a process with uncertain outcomes, while an outcome is any possible result. The sample space is the set of all possible outcomes. Fundamental counting principles state that if one event can occur in m ways, a second in n ways, and a third in p ways, the total number of outcomes is m x n x p. Probability is calculated by dividing the number of favorable outcomes by the total number of possible outcomes.

2. Probability is the branch of mathematics
concerning numerical descriptions of how
likely an event is to occur, or how likely it is
that a proposition is true.

3. Sample Space,
Events,
Outcomes, and
Experiments

4. Definition
Experiment - a process that has a number of distinct possible
outcomes in which the result cannot be predicted with certainty
Outcome - any possible result of the experiment
Sample Space - the set of all possible outcomes of an
experiment

5. Let’s Try
List the elements or the results when you perform the
following activities.
1. Tossing a COIN

6. Let’s Try
List the elements or the results when you perform the
following activities.
2. Rolling a die

7. Let’s Try
List the elements or the results when you perform the
following activities.
3. Ask the birth month of persons you met in the school
campus

8. Examples
List all the possible outcomes for the experiment of tossing two
coins (a 5-peso coin and a 10-peso coin)

9. Examples
List all the sample space when a pair of dice are tossed

12. Seatwork
1. List all the possible outcomes for the experiment of tossing
three coins (a 1-peso, 5-peso and 10-peso coin)
2. List the sample space and give the total number of possible
outcomes for drawing a ball at random from a box
containing 3 identical red balls and 4 identical green balls
3. List the sample space for a three-digit number formed from
the digits 1, 9, 5, and 3 with no digit to be used more than
once

13. Suppose that you have to choose on what Outfit to
wear, How many options do you have?

14. Fundamental Counting Principles
If one thing can occur in m ways and a second thing can
occur in n ways, and a third thing can occur in p ways, and so
on, then the sequence of things can occur in m x n x p … ways

17. Examples
Double O’s cafe serves three desserts: a cake, a
salad, and a pie. They also serves four beverages:
cola, coffee, tea and juice. Suppose you choose
one dessert and one beverage. How many
possible outcomes are there?

18. Examples
Rene Alarcon is a disc jockey. He chooses different
types of records for each hour of his three hour
program. The possible choices are listed below. How
many possible outcomes are there?
First Hour: Rock , Folk
Second Hour: Instrumental, Jazz, Pop
Third Hour: Opera, Classical, Rap, Techno

19. Examples
A plate number is made up of three letters from the
English alphabet followed by a three-digit number. How
many plate numbers are possible to form if:
a. The letters and digits can be repeated in the same
plate number
b. The letters and digits cannot be repeated in the
same plate number

23. Examples
In tossing two dice, what is the probability of the
event?
a. A sum of “7”
b. A sum of “5”

25. Examples
A committee of two is to be chosen at random from a
group of 5 students consisting of 3 boys and 2 girls. What
is the probability that a committee
a. Of two boys will be chosen?
b. Of two girls will be chosen?
c. Consisting of 1 boy and 1 girl will be chosen?