3. Sample Space
List the sample space of the
following experiments.
1. Tossing two coins
2. Rolling a die and tossing a coin
at the same time.
3. Getting a red ball when two balls
are randomly picked from a box
containing 5 red balls and 6 blue
balls.
4. Random Variable
A random variable is a
function that associates a
real number to each element
in the sample space. It is a
variable whose values are
determined by chance.
5. Suppose you are to test three random
eggplants from a harvest to see if there
are worms in it. You want to find out the
number of eggplants attacked by worms.
Use W to represent if there is a worm
attack in an eggplant and N if there is
none. Let Z be the random variable
representing the number of eggplants
attacked by worms. Find the values of the
Let’s try!
6. Three coins are tossed. Let X be the random
variable representing the number of heads
occur. Find the values of the random variable
X.
Practice!
7. 1. A dog gave birth to a litter of six puppies.
Three of them are male while the rest are female.
If you are to be given three of these puppies at
random, list all the elements of the sample space
using the letters M and F for male puppies and
female puppies, respectively. Then assign a
value to the random variable X representing the
number of male puppies you receive.
Activity #1!
8. 2. A pair of dice is rolled. Let X be the random
variable representing the number of getting even
numbers. Find the values of the random variable
X.
Activity #1!
9. A random variable is a discrete random
variable if its set of possible outcomes is
countable.
A random variable is a continuous random
variable if it takes on values on a
continuous scale.
10. Discrete Random Variable
• the number of vowels in the English alphabet
• the number of honor students in a class
• the number of satellites orbiting the Earth
• count of words encoded per minute
• yearly death due to cancer
Examples:
11. Continuous Random Variable
• amount of sugar in a cup of coffee
• time needed to solve a Rubik’s cube
• volume of diesel used in a trip
• length of a cellphone charger
• distance between two barangays
Examples:
12. • the blood pressures of a group of students the day
before the final exam
• the height of a player on a basketball team
• the number of coolers sold in a cafeteria during
lunch
• the temperature in degrees Celsius on February 5th
in Masinloc, Zambales
• the number of goals scored in a soccer game
Let’s try!
13. • the speed of a car
• the distance a golf ball travels after being hit
• the weight of a rhinoceros
• the number of female STEM students
• the number of deaths per year attributed to lung
cancer
• the amount of paint utilized in a building project
• the number of new teachers in SASMA
Let’s try!
14. • the number of defective computers produced by a
manufacturer
• the weight of newborns each year in a hospital
• the number of diamond suits in a deck of cards
• the number of dropouts from SASMA in ten years
• the number of Andreans with Android phones
• the time needed to finish the test
• the number of Olympic gold medalists
Let’s try!
15. • the number of broken chairs in Kinder Garten
• the number of Math club members
• the weight of 10,000 people
• the number of children in a family
• the number of defective bulbs in a box of 10
• the amount of rain in a day
• the length of hairs on a horse
Let’s try!
16. Event (E) Probability (P)
Getting a prime number in a single roll of
die
𝟏
𝟐
Getting a red queen when a card is drawn
from a deck
𝟏
𝟐𝟔
Getting a numbered card when a card is
drawn from the pack of 52 cards
𝟗
𝟏𝟑
Getting a sum of 7 when two dice are
thrown
𝟏
𝟔
17. Probability
Distribution or
Probability Mass
Function
A discrete probability
distribution or a probability
mass function consists of
the values a random variable
can assume and the
corresponding probabilities
of the values.
18. Determine whether the distribution represents a
probability distribution. Explain your answer.
Practice!
X 1 5 8 7 9
P(X)
𝟏
𝟑
𝟏
𝟑
𝟏
𝟑
𝟏
𝟑
𝟏
𝟑
19. Determine whether the distribution represents a
probability distribution. Explain your answer.
Practice!
X 0 2 4 6 8
P(X)
𝟏
𝟔
𝟏
𝟔
𝟏
𝟑
𝟏
𝟔
𝟏
𝟔
20. Determine whether the given values can serve as
the values of a probability distribution of the
random variable X that can take on only the
values 1, 2 and 3. Explain your answer.
1. P(1) = 0.08, P(2) = 0.12, P(3) = 1.03
2. P(1) =
9
14
, P(2) =
4
14
, P(3) =
1
14
Practice!
21. Suppose three cellphones are tested at random.
Let D represent the defective cellphone and N
represent the non-defective cellphone. Also, let Y
be the random variable representing the number
of defective cellphones. Find the values of the
random variable Y.
Practice!
