PPT on Q4 math 10

1. Illustrate the
Probability of a
Union of Two
Events
DEBBIE ANN LAOGAN
PRE-SERVICE TEACHER

2. OBJECTIVES
At the end of the session, at least 80% of the students
should be able to:
a. Illustrate the probability of a union of two events -
Mutually exclusive and Non-Mutually exclusive events;
b. Find the probability of a union of two events - Mutually
exclusive and Non-Mutually exclusive events; and
c. Engage in hands-on and group activities to simulate and
experiment with the probability of a union of two events.

3. FIND ME!
(CHECKING OF ASSIGNMENT)

4. ______a. A king or an ace?
______b. A number card or an ace?
______c. A black card or a diamond?
______d. A number 3 or a heart?
______e. A black card or 10 of spades?
______f. A face card or a diamond?
A card is drawn at random from a 52 – deck of
cards. Find the Probability of getting:

5. A card is drawn at random from a 52 – deck of cards. Find the
Probability of getting:
a. A king or an ace?
4
52
+
4
52
=
8
52
=
2
13
b. A number card or an ace?
36
52
+
4
52
=
40
52
=
10
13
c. A black card or a diamond?
26
52
+
13
52
=
39
52
=
3
4
d. A number 3 or a heart?
4
52
+
13
52
−
1
52
=
16
52
=
4
13
e. A black card or 10 of spades?
26
52
+
1
52
−
1
52
=
26
52
=
1
2
f. A face card or a diamond?
12
52
+
13
52
−
3
52
=
22
52
=
11
26

6. Renz rolled a fair die and wished to find the
probability that
1.“the number that turns up is odd or even”.
2.“the number that will turn is even or greater
than 3”.

7. PROBABILITY OF THE UNION OF:
 Mutually exclusive events - are those events that do
not occur at the same time. In other words, mutually
exclusive events are called disjoint events.
 If two events are considered disjoint events, then the
probability of both events occurring at the same time
will be zero.
P(A and B) = 0 “The probability of A and B
together equals 0 ”impossible”

8.  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) or P(A  B) = P(A) + P(B)

9.  Non-mutually exclusive events – are events that can
happen at the same time. In other words, non-
mutually exclusive events are called joint events.
 The probability of the union of two events A and B
written as P(AB) or P(A or B) is equal the to sum of
the probability of event A P(A) and the probability of
event B P(B) minus the probability of event A and B
occurring together P(AB). In symbols,
P(AB) = P(A) + P(B) – P(AB)

11. Renz rolled a fair die and wished to find the
probability that
1.“the number that turns up is odd or even”.
Given: S = 1,2,3,4,5,6 A = 1,3,5 B = 2,4,6
Formula: P(AB) = P(A) + P(B)
Solution: P(AB) =
3
6
+
3
6
=
6
6
𝑜𝑟 1

12. Renz rolled a fair die and wished to find the
probability that
2.“the number that will turn is even or greater
than 3”.
Given: S = 1,2,3,4,5,6 A = 2,4,5 B = 4,5,6 (AB) = 4,6
Formula: P(AB) = P(A) + P(B) – P(AB)
Solution: P(AB) =
3
6
+
3
6
−
2
6
=
4
6
𝑜𝑟
2
3

13. A pair of dice is rolled. What is the probability
that the two dice show the same number or that
the sum of the numbers is less than 7?

14. A pair of dice is rolled. What is the probability
that the two dice show the same number or that
the sum of the numbers is less than 7?
Given: A = 1-1,2-2,3-3,4-4,5-5,6-6
B = 1-1,1-2,1-3,1-4,1-5,2-1,2-2,2-3,2-4,3-1,3-2,3-3,4-1,4-2,5-1
(AB) = 1-1,2-2,3-3
Formula: P(AB) = P(A) + P(B) – P(AB)
Solution: P(AB) =
6
36
+
15
36
−
3
36
=
18
36
=
1
2

15. A pair of dice is rolled. What is the probability
that the two dice show the same number or that
the sum of the numbers is less than 8?

16. A pair of dice is rolled. What is the probability
that the two dice show the same number or that
the sum of the numbers is less than 8?
Given: A = 1-1,2-2,3-3,4-4,5-5,6-6
B = 1-1,1-2,1-3,1-4,1-5,1-6,2-1,2-2,2-3,2-4,2-5,3-1,3-2,3-3,3-4,4-1,4-2,4-3,5-1,5-2,6-1
(AB) = 1-1,2-2,3-3
Formula: P(AB) = P(A) + P(B) – P(AB)
Solution: P(AB) =
6
36
+
21
36
−
3
36
=
24
36
=
2
3

17. THINK-PAIR-SHARE

18. A pair of dice is rolled. What is the probability
that the two dice show the same number or
that the sum of the numbers is less than 5?

19. A pair of dice is rolled. What is the probability
that the two dice show the same number or
that the sum of the numbers is less than 5?
Given: A = 1-1,2-2,3-3,4-4,5-5,6-6
B = 1-1,1-2,1-3,2-1,2-2,3-1
(AB) = 1-1,2-2
Formula: P(AB) = P(A) + P(B) – P(AB)
Solution: P(AB) =
6
36
+
6
36
−
2
36
=
10
36
=
5
18

20. Can you cite an instance in your day-to-
day activities applying the probability of
union of two events?
At home
In school

21. LET’S SUM IT UP!
In solving the probability of the union of two events, if
the two sets do not have elements in common, use
Mutually exclusive events
P(A or B) = P(A) + P(B) or P(A  B) = P(A) + P(B)
If the two sets have elements in common, use Non-
mutually exclusive events
P(A or B) = P(A) + P(B) – P(AB)

22. IT’S YOUR TURN!
In one half crosswise sheet of paper, solve the following
problem completely. Show complete solution. 5 points each.

23. 1.Simon rolled a fair die and wished to find the
probability that
“the number that will turn is odd or greater
than 4”.
2. If a card is drawn at random from a 52-deck
of cards. Find the probability of getting a heart
or a diamond card.

24. HOME LEARNING TASK
Direction: Solve the following completely.
1. A card is drawn at random from a standard
deck of cards. What is the probability of
drawing a queen or a king?
2. A die is rolled. What is the probability of
getting a prime number or an odd number?

25. THANK YOU!