This document discusses probability concepts including intersection, union, and complement of events. It provides examples to illustrate finding the probability of intersection (P(A ∩ B)), union (P(A ∪ B)), and complement (P(A')) of events. One example calculates the probabilities of: P(B), P(V), P(B ∩ V), P(B ∪ V), and P(B' ∩ V') given P(B)=0.3, P(V)=0.2. It also asks students to practice calculating these probabilities in groups for events with given probabilities.

1. ACTIVITY
Extra-curricular activities participated by senior students
1. How many students are in the senior class?
2. How many students participate in athletics?
3. Is a student randomly chosen, what is the probability
that the student participates in athletics or drama?
4. Is a student randomly chosen, what is the probability
that the student participates in drama and band?

2. PROBABILITY OF
INTERSECTION
AND UNION OF
EVENTS

3. Learning Objectives
a. identify the probability of intersection,
union and complement of events;
b. find the probability of intersection, union
and complement of an events; and
c. relate the probability intersection, union and
complement of an events to a real-life
situation.

4. PROBABILITY
A branch of mathematics that deals with
the measurement of likelihood or chance
that an event will occur.
Can be written as fraction, decimal and
percentage.

5. PROBABILITY
The probability that an event will happen
is from 0 to 1.
If a particular event is impossible to
happen, then P(E) = 0.
If a particular event is certain to happen
then P(E) = 1.

6. Intersection of Events
These are the elements found to both
events A and B, written as A Ո B.

7. Example:
Is a student randomly
chosen, what is the
probability that the
student participates in
drama and band?
(Drama and Band) = 30
P(Drama and Band) =
𝑛(𝐸)
𝑛(𝑆)
=
30
345
or
2
23

8. Union of Events
These are the elements found in event A,
event B, or in both A and B, can be
written as A Ս B

9. Example:
Is a student randomly
chosen, what is the
probability that the
student participates in
athletics or drama?
(Athletics or Drama) = 227
P(Athletics or Drama) =
𝑛(𝐸)
𝑛(𝑆)
=
227
345

10. Complement of an Event
The set of all outcomes that are NOT in
the event. P(A՚) = 1 – P(A)

11. Example:
Is a student randomly
chosen, what is the
probability that the
student do not
participate in athletics
or drama?
(Athletics or Drama)՚ = 118
P(Athletics or Drama)՚ =
𝑛(𝐸)
𝑛(𝑆)
=
118
345
P(Athletics or Drama)՚ = 1 - P(Athletics Ս Drama)
= 1 -
227
345
=
118
345

12. Example:
a. P(B)
b. P(V)
c. P(B Ո V)
d. P(B Ս V)
e. P(B՚Ո V՚)
a.P(B) =
b.P(V) =
0.3 + 0.2 = 0.5
0.4 + 0.2 = 0.6

13. Example:
a. P(B)
b. P(V)
c. P(B Ո V)
d. P(B Ս V)
e. P(B՚Ո V՚)
c. P(B Ո V) =
d. P(B Ս V) =
0.3
0.3 + 0.2 + 0.4 = 0.9

14. Example:
a. P(B)
b. P(V)
c. P(B Ո V)
d. P(B Ս V)
e. P(B՚Ո V՚)
c. P(B՚Ո V՚) = 0.1
c. P(B՚Ո V՚) = 1 – P(B Ս V)
= 1 – 0.3+0.2+0.4
= 1 – 0.9 = 0.1

15. Lets Try!
Work with your
seatmate.
a. P(B)
b. P(V)
c. P(B Ո V)
d. P(B Ս V)
e. P(B՚Ո V՚)
40% 20%
10%

16. GROUP WORK.

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

18. Review!
• The probability that an event will happen is from 0 to 1.
• Probability of Event – P(E) =
𝑛(𝐸)
𝑛(𝑆)
• Probability of Intersection of events – P(B Ո A) =
𝑛(𝐸)
𝑛(𝑆)
• Probability of Union of events – P(B Ս A) =
𝑛(𝐸)
𝑛(𝑆)
• Probability of Complement of events – P(A՚) = 1 – P(A)

19. Quiz!
Identify the following.
1. The probability that an event will happen is
from .
2. – P(E) =
𝑛(𝐸)
𝑛(𝑆)
3. – P(B Ո A) =
𝑛(𝐸)
𝑛(𝑆)
4. – P(B Ս A) =
𝑛(𝐸)
𝑛(𝑆)
5. – P(A՚) = 1 – P(A)

20. Assignment:
SOLVE the following. (1/2 crosswise)
A bowl contains 15 chips numbered 1 to 15. If a
chip is drawn randomly from the bowl, what is
the probability that it is
a. 7 or 15
b. 5 or a number divisible by 3?
c. even or divisible by 3?
d. a number divisible by 3 or divisible by 4?