This document discusses mutually exclusive events and not mutually exclusive events. Mutually exclusive events cannot occur at the same time, like getting a 3 or a 2 when rolling a die. Not mutually exclusive events can occur at the same time, like drawing a face card or a black card from a standard deck of cards. The document provides examples and explanations of calculating probabilities for these different types of events.

1. Mutually Exclusive Events and
Not Mutually Exclusive
Events

5. Two events may or
may not happen at
the same time.

7. What is a Mutually
Exclusive Event?
- Events that do not have
the same elements
- Events that can’t happen
at the same time

9. Example
1.Getting a 3
or getting a 2
in rolling a
die.

10. 2. Getting a red
card and a
black card in a
standard deck
of cards

11. 3.A card is drawn from a deck of standard playing cards.
Event A: An ace is drawn.
Event B: A king is drawn.

13. 2. A rectangular box contains balls numbered {1, 2,
3, … , 18, 19, 20}. If a ball is randomly drawn from
a box,
a. what is the probability that it is 3 or 15?
•Solution:
1, 2,3,4,5,6,7,8,9,10,11,12,13,14,15,…20
P( A or B) = P( A ) + P( B)
P( 3 or 15 ) = P( 3 ) + P( 15)
= 1/20+ 1/20
P(3 or 15) = 2/20 or 1/10

14. Not Mutually
Exclusive
Events
-Events that have outcomes
in common.

15. Example:
From a deck of
52 cards, what is the
probability that the
card is a face card or
a black card?

18. •A rectangular box contains balls numbered {1, 2,
3, … , 18, 19, 20}. If a ball is randomly drawn
from a box, what is the probability that it is a
number divisible by 4 or a number divisible by 5?
Solution:
1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20
No. divisible by 4 – ( 4,8,12,16,20)
No.divisible by 5 –( 5,10,15,20)
P ( A or B) = P( A) + P ( B ) – P ( A and B)
P(no. div.by 4 or no. div. by 5 ) = 5/20 + 4/20 – 1/20
= 8/20
P( no.div.by 4 or no.div.by 5 ) =2/5

24. Determine whether each of the following event is
mutually exclusive or not mutually exclusive
events. Then find its probability.
1. Getting a 6 or a number divisible by 3 when rolling a
die
2 Getting 3 tails or 1 head when four coins are
dropped onto the floor.
3. Selecting a blue or a red when picking a ball from a
box that contains 10 blue balls and 15 red balls
4. Selecting a letter A from the word PROBABILITY or
a vowel
5. Getting a head or a tail when tossing a coin