Review:
Identify the experiment, outcome, sample space, and event in the following
situations.
1. What is the likelihood of the die landing on a number lower than 4 when thrown?
a. Experiment:
b. Outcome:
c. Sample space:
d. Event:
PROBABILITY - is used to explain how likely or unlikely an event is to happen. Not
all events are certain, some may happen, some may not.
Probability of any event is a number (either a fraction, a decimal, or a percent)
from 0 to 1.
Before using numbers,
Probability Line
probability can be
described using words such
as:
 Impossible
 Unlikely
 Equally likely
 Likely
 Certain
Examples:
Where does each situation lie on the probability line?
1. Getting a head when tossing a fair coin
2. Drawing a heart from a deck that contains only spades
3. Rolling a number less than 5 on a standard die
4. Getting a 7 when rolling a standard die
5. Tossing two coins and getting two heads
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ACTIVITY #1:
Where does each situation lie on the probability line?
1. Choosing a day at random and it is
6. Selecting a male student from a
a weekday
class with an equal number of boys
2. Drawing the ace of spades from a
and girls
standard deck
7. The sun rising tomorrow
3. Getting either a red or black card
8. Drawing a red marble from a box of
from a standard deck
3 red and 3 blue marbles.
4. Tossing a coin and getting both
9. Getting two heads in tossing two
heads and tails at the same time
coins
5. Drawing a red card from a deck
10. Obtaining an even number in
with more red cards than black cards
rolling a die.
Probability is used in daily situations such as:



Weather forecasts (chance of rain)
Games and sports (coin toss, dice, cards)
School situations (chance of being chosen)
Probability does not guarantee an outcome. Even if an event has a high probability,
it does not mean it will definitely happen. Likewise, an event with a low probability
can still occur.
Importance of probability
- helps us predict outcomes, make better decisions, and understand uncertain
situations.
SYSTEMATIC LISTING- is a step-by-step method to make sure all outcomes are
included. It helps prevent missing or repeating results.
Types of Systematic Listing
1. Organized / Simple List
Outcomes are listed in a straight line, usually when there are few possibilities.
Example: Toss one coin → Head, Tail
Roll a die → 1, 2, 3, 4, 5, 6
Example: Toss two coins
Coin 2
T
H
Coin 1
2. Table / Grid
Useful when two experiments happen
together.
T
T, T
T, H
H
H, T
H, H
3. Tree Diagram
Shows all possible outcomes visually using
branches. Great for compound experiments.
Example: Toss a coin and roll a die
Why use different types



List: Simple and quick for small
experiments.
Table: Organizes two-step experiments
clearly.
Tree diagram: Helps visualize complex
experiments and combinations.
ACTIVITY #2:
List all outcomes using a list, table, and tree diagram.
1. Suppose that a family has two children. Find all the possible outcomes for the
genders of the children.
2. List all the 2-digit numbers that can be formed from the set {3, 6, 9}