Probability-of-Simple-and-Compound-Events.pptx

TERMS RELATED TO PROBABILITY
A. EXPERIMENT –
AN ACTIVITY
WHICH COULD BE
REPEATED, AND
WHICH HAS WELL-
DEFINED RESULTS
B. OUTCOME –
A RESULT OF
AN
EXPERIMENT
C. SAMPLE
SPACE – A SET
OF ALL
OUTCOMES IN
AN
EXPERIMENT
D. EVENT – A
SUBSET OF THE
SAMPLE SPACE

TERMS RELATED TO PROBABILITY
The “cardinality” of an event is the number of elements
in the set of all possible outcomes. The cardinality of a
set is denoted by vertical bars similar to the notation for
absolute values.
A set without any element is an “empty set” and usually
denoted by or { }. The cardinality of an empty set is
∅
zero, | |= 0.
∅

EXAMPLE
a. Experiment: A die is rolled once.
b. Event: “Getting a 3” and “Getting
a 2” are some of the simple events.
c. Outcomes: If you roll a die once,
then, you have 1, 2, 3, 4, 5, or 6.
d. Sample Space: Write all the
outcomes as a set, so it is {1, 2, 3,
4, 5, 6}.

EXAMPLE
There were 3
blue balls and 2
red balls from a
box. You are to
get three balls at
the same time
from this box.
What is the
probability of
getting 1 blue
ball and 2 red
balls?
a. Experiment: Get three balls
at the same time from the box
b. Event: Getting 1 blue ball and
2 red balls
c. Outcomes: {RRB, RRB, RRB}
d. Sample Space: {BBB, BBR,
BBR, BBR, BBR, BBR, BBR, RRB,
RRB, RRB}

Think-Pair-Share
Identify the experiment, event, sample space, and the cardinality
of the sets.
1. Getting a number less than 5 in rolling a die.
2. A colored spinner is spun once. It has seven different colors
of the rainbow with equal area. What is the probability that the
pin will land on blue?
3. Getting a sum of 8 in rolling two dice.
4. Getting two heads in tossing two coins once.

Your Turn
Identify the experiment, event, sample space, and
the cardinalities.
1. Getting a number divisible by 3 in a single roll
of die
2. Picking an odd number ball from a box with 15
balls numbered 1-15.
3. Getting tails in tossing two coins.

Evaluation
Direction: Read the following question below and encircle the letter of the correct answer.
1.Which of the following denotes the results of an experiment?
a. Outcomes b. event c. experiment d. sample space
2. It is a subset of sample space.
a. Outcomes b. experiment c. event d. sample space
3. It is a set of all outcomes in an experiment
a. Outcomes b. experiment c. event d. sample space
4. A process that produces an outcome which can be random or not.
a. Experiment b. outcomes c. event d. sample space
5. In throwing two die once, what is the cardinality of the sample space?
a. 6 b. 12 c. 24 d. 36

EXAMPLE
In rolling a die, what is
the probability of
getting a
1. 3
2. an even number

SIMPLE
EVENTS
Probability of Simple Events: If each of
the outcomes in a sample space is
equally likely to occur, then the
probability of an event E, denoted as
P(E) is given by
or

Review
PROBABILITY
It is the chance of
occurrence of an event
among a large number of
possibilities.
a. Experiment
b. Outcomes
c. Event
d. Sample Space

PROBABILITY
The probability of an event is the ratio of the number of
favorable outcomes to the number of possible outcomes. It can
be expressed as a fraction, a decimal, or a percent.
The value of a probability is a number between 0 and 1
inclusive.
Impossible Events
An event which has no
chance of occurring.
Certain Events
An event that will surely
come out in an experiment.

Activity 1
Determine if the given events are (a)
certain, (b) likely or unlikely to happen,
and (c) impossible.
1. Classes will be suspended tomorrow.
2. You will win in the lottery without
buying any ticket.
3. You will get younger in 10 years.
4. You will pass Mathematics subject.
5. The sun will rise from east.

SIMPLE EVENTS COMPOUND EVENTS
EVENTS

SIMPLE EVENT (ELEMENTARY EVENT) – It is determined by the
outcome of one trial in the experiment.
Probability of Simple Events– If each of the outcomes in a sample
space is equally likely to occur, then the probability of an event E,
denoted as P(E) is given by:

Illustrative Examples
1.Find the probability of getting a number less than 5 in rolling a
fair die.
2. What is the probability of drawing a white marble from a bag
containing 3 red marbles and 1 white marble?

3. A spinner is spun once. It is divided into 8 equal parts with
four different colors shown below. What is the probability
that the pin will land on blue?

4. What is the probability that you will pull a heart out of a
standard deck of cards?
5. Find the probability of drawing a face card in a standard
deck of cards.

COMPOUND EVENTS – These are events which
consist of more than one outcome. It consists of
two or more simple events.

Which road will you
take? Left or right?
ACTIVITY 2

Playing Mobile
Legends or
studying your
lesson?

Mutually Exclusive Events
– events that have no
outcomes in common. This
also means that if two or
more events are mutually
exclusive, they cannot
happen at the same time.
Example 6
A = “getting an even number in
rolling a fair die”
B = “getting an odd number in
A={2, 4, 6}
B={1,3, 5}

Not Mutually Exclusive
Events
– events that have
outcomes in common.
Events can happen at the
same time.
Example 7
A = “getting an even number in
B = “getting a number greater
than 3”
A={2, 4, 6}
B={4, 5, 6}

Directions: Determine if the desired events are mutually
exclusive or non-mutually exclusive.
1. Event A: toss a coin and get “heads”
Event B: toss a coin and get “tails”
2. Event A: roll a fair die and get a “1”
Event B: roll a fair die and get a “6”
3. A card is drawn from a standard deck of playing cards.
a. P (a black card or a face card)
b. P (a spade or a heart)
c. P (an ace or a red card)
d. P (a queen or a diamond)
e. P (a club or a red card)

PROBABILITY OF MUTUALLY EXCLUSIVE
AND NOT MUTUALLY EXCLUSIVE EVENTS
ADDITION RULE FOR PROBABILITIES
If two events, A and B, are mutually exclusive, then the probability that
either A or B occurs is the sum of their probabilities. In symbols,
P (A or B) = P(A) + P(B).
If two events, A and B, are not mutually exclusive, then the probability that
either A or B occurs is the sum of their probabilities decreased by the probability of
both occurring. In symbols,
P (A or B) = P(A) + P(B) – P (A and B).

Solve the following problems.
1. You spin a wheel which has eight equal sectors (A, B, C, D, E, F, G,
H). What is the probability that the pin will land on:
a.D or a vowel?

1. You spin a wheel which has eight equal sectors (A, B, C, D, E, F, G,
H). What is the probability that the pin will land on:
b. Consonant or letter of the word BAG?

Solve the following problem.
2. You have equally likely chance of choosing any integer from 1
through 20. What is the probability that it is a perfect square or
divisible by 4?

3.Rhian likes to wear colored shirts. She has 15 shirts in the closet. Five
of these are blue, four are in different shades of red, and the rest are
of different colors. What is the probability that she will wear a blue or a
red shirt?

4.A card is randomly selected from a standard deck of 52 cards. What is
the probability that it is:
a.a king or an ace?
b.a red card or a numbered card?

1. In rolling a fair die, what is the probability of:
a. getting 3 or 6?
b. getting an odd or divisible by 5?
2. A card is randomly drawn from a standard deck of cards. What is
the probability that the card is:
a. jack or heart?
b. 5 or queen?
c. spade or face card?
3. A coin is tossed once. Find the probability of getting a head or tail?

What’s the
difference?
Fred has a bag
of different
chocolates, he
picked one but
do not like it, so
he returned it
on the bag
before picking
another
chocolate.
Fred has a bag
of different
chocolates, he
picked one
dark chocolate
ate it, and then
pick another
chocolate.

INDEPENDENT
EVENTS
Two events are independent if the
occurrence of one of the events give us
no information about whether the other
event will occur; that is, the events have
no influence on each other.
Example 8: Suppose that a coin is
tossed once and a die is rolled once,
the event that a coin shows up tail and
the event that a die shows up a 2 are
independent events.

DEPENDENT
EVENTS
When the outcome of one event
affects the outcome of another event,
they are dependent events.
Illustrative Example 5: If there is
a box containing 5 white marbles
and 4 black marbles, the
probability of drawing 1 white
marble and 2 black marbles in
succession without replacement.

Determine if the event is dependent or independent.
Write your answer on your show-me board.
1. A bag contains 6 black marbles, 9 blue marbles, 4 yellow marbles, and 2 green
marbles. A marble is randomly selected, replaced, and a second marble is
randomly selected.
2. A box of candies contains 10 Yema candies, 8 Sampaloc candies, and 6 Bucayo
candies. Eduardo randomly chooses a candy, eats it, and then randomly chooses
another candy.
3. A toy box contains 12 toys, 8 stuffed animals, and 3 board games. Maria randomly
chooses 2 toys for the child she is babysitting to play with.
4. Two cards have been drawn from the deck of 52cards without replacing the first
one back.
5. Nick has 4 black pens, 3 blue pens, and 2 red pens in his school bag. Nick
randomly picks two pens out of his school bag. What is the probability that Nick chose
two blue pens, if he replaced the first pen back in his pocket before choosing a
second pen?

PROBABILITY OF INDEPENDENT AND
DEPENDENT EVENTS
MULTIPLICATION RULE FOR PROBABILITIES
If two events, A and B, are independent, the probability of both events
occurring is the product of the probability of A and the probability B. In symbols,
If two events, A and B, are dependent, then the probability of both events
occurring is the product of the probability of A and the probability of B after A occurs.
In symbols,

A box contains 5 green,6 yellow and 4 blue balls. Find the
probability of selecting two balls (a yellow on the first and able on
the second) if selection is done with replacement.

A box contains 9 tickets numbered 1 to 9 inclusive. If three tickets are
drawn from the box one at a time without replacement, find the probability
that they are alternately
a. odd, eve, odd
b. even, odd, even

Nick has 4 black pens, 3 blue pens, and 2 red pens in his school bag.
Nick randomly picks two pens out of his school bag. What is the
probability that Nick picked two blue pens, if he replaced the first pen
back in his school bag before picking a second pen?

Answer the following.
1. What is the probability of getting a composite number on the first roll of a
die and getting a prime number on the second roll?
2. There are 5 red roses, 3 yellow roses, and 8 white roses in a tray. If
Roxanne picked 2 roses one after the other without replacing, then what is
the probability of picking a white rose first and a red rose next?
3. 4 red cubes and 4 white cubes are there in a basket. If two cubes are
drawn at random, then what is the probability that the first one is white and
the second one is red?
4. Dhana has 4 brown, 5 violet, and 3 pink t-shirts. If he selects 2 t-shirts one
after the other without replacement, then what is the probability that both are
violet in color?
5. There are 6 pink and 8 white balls in a bag. If two balls are drawn after the
other, then what is the probability of getting a pink ball first and white ball
next, if the first ball drawn is replaced?

References:
Callanta, M. M., Canonigo, A. M., Chua, A. I., Cruz, J. D.,
Esparrago, M. S., Garcia, E. S., Magnaye, A. N., Orines, F.
B., Perez, R. S., Ternida, C. S. (2015). Mathematics - Grade
10 Learner’s Module First Edition. DepEd-IMCS.
Banaag, G. D., Quan, R. A. (2013). Global Mathematics 10.
The Library Publishing House, Inc.

Learning Objectives
1. Identify the different types of
events.
2. Solve the probability of simple
events.
3. Solve the probability of mutually
and not mutually exclusive events.
4. Solve the probability of
independent and dependent
events.

Probability-of-Simple-and-Compound-Events.pptx

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