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Mutually Exclusive Events and
Not Mutually Exclusive
Events
Two events may or
may not happen at
the same time.
What is a Mutually
Exclusive Event?
- Events that do not have
the same elements
- Events that can’t happen
at the same time
Example
1.Getting a 3
or getting a 2
in rolling a
die.
2. Getting a red
card and a
black card in a
standard deck
of cards
3.A card is drawn from a deck of standard playing cards.
Event A: An ace is drawn.
Event B: A king is drawn.
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
Not Mutually
Exclusive
Events
-Events that have outcomes
in common.
Example:
From a deck of
52 cards, what is the
probability that the
card is a face card or
a black card?
•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
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
mutually and nonmutually event.pptx

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mutually and nonmutually event.pptx

  • 1. Mutually Exclusive Events and Not Mutually Exclusive Events
  • 2.
  • 3.
  • 4.
  • 5. Two events may or may not happen at the same time.
  • 6.
  • 7. What is a Mutually Exclusive Event? - Events that do not have the same elements - Events that can’t happen at the same time
  • 8.
  • 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.
  • 12.
  • 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?
  • 16.
  • 17.
  • 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
  • 19.
  • 20.
  • 21.
  • 22.
  • 23.
  • 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