MATH10

1. Let`s Recall:
1. MALSEP ESCAP - a set of all possible
outcomes
2. NETEV - subset of a sample space.
3. ALCDINYARIT – number of elements in
a sample space or event.
4. ILITPYOBARB – the chance or likelihood
that an event will happen.

2. Activity
1. A die is rolled once. Find the
probability of obtaining
a) a 6
b) a 3
c) an even number

3. Activity
1. Toss the coin once. Find the
probability of obtaining
a) a head
b) a tail

4. INTRODUCTION
TO PROBABILITY OF
AN EVENTS

5. Learning Objectives
a) differentiate simple event and
compound events;
b) find the probability of simple event
and compound events; and
c) express appreciation on the
importance of probability in real
life.

6. WHAT IS PROBABILITY?
Probability is a branch of mathematics
that enables us to predict the
occurrence of an event as a result of an
experiment.
Probability of an event can be written
in fraction, decimal, and percentage
form.

7. WHAT IS PROBABILITY?
Probability is a branch of mathematics that
enables us to predict the occurrence of an
event as a result of an experiment.

8. WHAT IS PROBABILITY?
Experiments are activities which could be
repeated, and which have a well-defined
results.

9. WHAT IS PROBABILITY?
Experiments are activities which could be
repeated, and which have a well-defined
results.
Outcomes – the results of an experiments
Sample space – the set of all outcomes in
an experiment. It usually denoted as letter
S, can be written using set notation { }.
Event – is a subset of a sample space.

10. EXAMPLE
“TOSSING A COIN”
Possible outcomes – Head, Tail
Sample space – S={Head, Tail} or S={H,T}
Events – showing a Head, showing a Tail

11. EXAMPLE
“ROLLING A DIE”
Possible outcomes – 1, 2, 3, 4, 5, 6
Sample space – S={1, 2, 3, 4, 5, 6}
Events – getting a number 4
getting an odd number

12. Probability of an Events
P(E) =
𝑁𝑢𝑚𝑏𝑒𝑟 𝑜𝑓 𝑤𝑎𝑦𝑠 𝑡ℎ𝑎𝑡 𝑎𝑛 𝑒𝑣𝑒𝑛𝑡 𝑜𝑐𝑐𝑢𝑟
𝑁𝑢𝑚𝑏𝑒𝑟 𝑜𝑓 𝑝𝑜𝑠𝑠𝑖𝑏𝑙𝑒 𝑜𝑢𝑡𝑐𝑜𝑚𝑒𝑠
or
P(E) =
𝑁𝑢𝑚𝑏𝑒𝑟 𝑜𝑓 𝑜𝑢𝑡𝑐𝑜𝑚𝑒𝑠 𝑖𝑛 𝑡ℎ𝑒 𝑒𝑣𝑒𝑛𝑡
𝑁𝑢𝑚𝑏𝑒𝑟 𝑜𝑓 𝑜𝑢𝑡𝑐𝑜𝑚𝑒𝑠 𝑖𝑛 𝑡ℎ𝑒 𝑠𝑎𝑚𝑝𝑙𝑒 𝑠𝑝𝑎𝑐𝑒

13. Probability of an Events
Simple Events
 Consist of single
outcome in the
sample space.
Example
 A die is rolled. What
is the probability of
getting a 3?
Compound Events
 It consists of two or
more simple events.
Example
 Find the probability
of getting a 6 and a
1 when the two
dice are rolled.

14. Probability of Simple Event
Example:
A die is rolled what is the probability of
obtaining:
a. a 7
b.An odd number
c. Not a 4
d.Number less than 7

15. Probability of Simple Event
Example:
A die is rolled what is the probability of
obtaining:
S = {1, 2, 3, 4, 5, 6}
P(E) =
𝑛𝑜.𝑜𝑓 𝑤𝑎𝑦𝑠 𝑒𝑣𝑒𝑛𝑡 𝑐𝑎𝑛 𝑜𝑐𝑐𝑢𝑟
𝑛𝑜.𝑜𝑓 𝑝𝑜𝑠𝑠𝑖𝑏𝑙𝑒 𝑜𝑢𝑡𝑐𝑜𝑚𝑒𝑠
a. a 7
b. An odd number

16. Probability of Simple Event
Example:
A die is rolled what is the probability of
obtaining:
S = {1, 2, 3, 4, 5, 6}
P(E) =
𝑛𝑜.𝑜𝑓 𝑤𝑎𝑦𝑠 𝑒𝑣𝑒𝑛𝑡 𝑐𝑎𝑛 𝑜𝑐𝑐𝑢𝑟
𝑛𝑜.𝑜𝑓 𝑝𝑜𝑠𝑠𝑖𝑏𝑙𝑒 𝑜𝑢𝑡𝑐𝑜𝑚𝑒𝑠
c. Not a 4
d. Number less than 7

17. Probability of Simple Event
Example:
A jar contains 7 green marbles , 5 red
marbles and 8 blue marbles. If a ball is
picked from the jar, what is the probability
of getting a blue marbles?

18. Probability of Simple Event
Example:
A jar contains 7 green marbles , 5 red
marbles and 8 blue marbles. If a ball is
picked from the jar, what is the probability
of getting a red marbles?

19. Probability of Simple Event
Example:
A jar contains 7 green marbles , 5 red
marbles and 8 blue marbles. If a ball is
picked from the jar, what is the probability
of getting a green marbles?

20. Probability of Compound Event
Example:
Find the probability of getting a 6 and
a 1 when two dice are rolled.
S = {(1, 1), (1, 2), (1, 3), … , ()}

21. Probability of Compound Event
Example:
Find the probability of getting a 6 and a 1 when
two dice are rolled.

22. Probability of Compound Event
Example:
Find the probability of getting a 6 and a 1 when
two dice are rolled.
Total no. of outcomes
in the sample space is
36.
Number of outcomes
in the event is 2.

23. Probability of Compound Event
Example:
A die is thrown, and a coin is tossed,
show all possible outcomes.
 List
Table
Tree Diagram

24. Activity
A school canteen serves lunch for students. A set of menu consists of 1
type rice, 1 type of viand, and 1 type of drink. The tree diagram below
shows the possible menu combinations.

25. Activity
Write your name and answers on a
½ crosswise.
Group 1 – no. 1 and 2
Group 2 – no. 3 and 4
Group 3 – no. 5 and 6
Group 4 – no. 7 and 8
Group 5 – no. 9 and 10

26. Why do you think is the
study of probability
important in making
decisions in real life?

27. Summarizes
Probability is a branch of mathematics that enables us to
predict the occurrence of an event as a result of an
experiment.
P(E) =
𝑁𝑢𝑚𝑏𝑒𝑟 𝑜𝑓 𝑤𝑎𝑦𝑠 𝑡ℎ𝑎𝑡 𝑎𝑛 𝑒𝑣𝑒𝑛𝑡 𝑜𝑐𝑐𝑢𝑟
𝑁𝑢𝑚𝑏𝑒𝑟 𝑜𝑓 𝑝𝑜𝑠𝑠𝑖𝑏𝑙𝑒 𝑜𝑢𝑡𝑐𝑜𝑚𝑒𝑠
or
P(E) =
𝑁𝑢𝑚𝑏𝑒𝑟 𝑜𝑓 𝑜𝑢𝑡𝑐𝑜𝑚𝑒𝑠 𝑖𝑛 𝑡ℎ𝑒 𝑒𝑣𝑒𝑛𝑡
𝑁𝑢𝑚𝑏𝑒𝑟 𝑜𝑓 𝑜𝑢𝑡𝑐𝑜𝑚𝑒𝑠 𝑖𝑛 𝑡ℎ𝑒 𝑠𝑎𝑚𝑝𝑙𝑒 𝑠𝑝𝑎𝑐𝑒
Simple Events consist of single outcome in the sample
space.
Compound Events It consists of two or more simple
events.

28. Quiz
1. How does a simple event differ from a
compound event?
2. In rolling a fair die once, what is the
probability of getting greater than 4?
3. A die is thrown, and a coin is tossed,
what is the probability of getting a 1 and
tail?

29. Assignment
A card is randomly drawn from a deck
of 52 cards. Find the probability that
the card drawn is
a. an ace
b. a black card
c. a red card or a spade