MATH 10 3RD QUARTER

1. Probability of Compound
Events

9. Finding Outcomes of more than
one event
• The total outcomes of each event are found by using a tree
diagram or by using the fundamental counting principle.
• Example:
At football games, a student concession stand sells
sandwiches on either wheat or rye bread. The sandwiches
come with salami, turkey, or ham, and either chips, a
brownie, or fruit. Use a tree diagram to determine the
number of possible sandwich combinations.

10. Probability of Compound Events
• A compound event consists of two or more simple
events.
• Examples:
rolling a die and tossing a penny
spinning a spinner and drawing a card
tossing two dice
tossing two coins

11. Probability of Compound Events
Example: List down the following
events for the coin-die experiment.
1. The event A in which
the coin comes up
Heads(H)

12. Probability of Compound Events
Example: List down the following
events for the coin-die experiment.
2. The event B in which
the coin comes up Tails(T)

13. Probability of Compound Events
Example: List down the following
events for the coin-die experiment.
3. The event C
comes up 1.

14. Probability of Compound Events
Example: List down the following
events for the coin-die experiment.
4. The event D
comes up 5.

15. Probability of Compound Events
Example: List down the following
events for the coin-die experiment.
5. The event F in
which die does not
come up 6.

16. Probability of Compound Events
Example: List down the following
events for the coin-die experiment.
6. The event H in
which the coin comes
up Heads and the die, a
number greater than 3.

17. Probability of Compound Events
Example: List down the following
events for the coin-die experiment.
7. The event I in which
the coin comes up Tails
and the die, an even
number.

18. Probability of Compound Events
ACTIVITY:
1. Four coins are tossed. List down the elements of
the following events.
A= Four Heads
B= Three Heads and one Tail

19. Probability of Compound Events
ACTIVITY:
2. A card is selected from an ordinary deck of
playing cards ( 52 pieces). Name the elements in
each of the given events.
A= the card selected is diamond.
B= the card selected is a seven.
C= the card selected is a queen.
D= the card selected is a King of Hearts.

20. Probability of Compound Events
ACTIVITY:
2. A card is selected from an ordinary deck of
playing cards ( 52 pieces). Name the elements in
each of the given events.
A= the card selected is diamond.
B= the card selected is a seven.
C= the card selected is a queen.
D= the card selected is a King of Hearts.

21. Compound Events
• When the outcome of one event does not affect the
outcome of a second event, these are called
independent events.
• The probability of two independent events is found
by multiplying the probability of the first event by
the probability of the second event.

23. Compound Event Notations

26. Events that cannot occur at the
same time are called mutually
exclusive.
Suppose you want to find the
probability of rolling a 2 or a 4 on a
die. P(2 or 4) Since a die cannot show
both a 2 and a 4 at the same time, the
events are mutually exclusive.

27. Problem-Solving:
1. Two dice are rolled. What is the probability of
getting :
a. A 4 or a 6
b. Not 3 or a 5

28. Problem-Solving:
2. There are 3 red pens, 4 blue pens, 2 black
pens, and 5 green pens in a drawer. Suppose you
choose a pen at random.
a. What is the probability that the pen chosen is
red or blue?
b. What is the probability that the pen chosen is
blue or green?
c. What is the probability that the pen chosen is
red or black?

29. ACTIVITY:

36. No common Elements

38. Have atleast
one common
element
between them

40. Directions: Based form the given pair of events in each item, write ME on the
space provided before each number if the outcomes in the events are
MUTUALLY EXCLUSIVE or MI if MUTUALLY INCLUSIVE.
____ 1. Choosing a 7 or choosing a diamond in a deck of cards.
____ 2. Choosing a 7 and a jack in a deck of cards.
____ 3. Rolling a number less than 4 or rolling a number greater than 4 in a die.
____ 4. Rolling a 2 or rolling an even number in a die.
____ 5. Rolling a 1 or rolling a prime number in a die.
____ 6. Choosing a day that begins with letter S or choosing a Sunday in a week.
____ 7. Choosing a weekday or choosing a weekend day in a week.
____ 8. Choosing a letter R or choosing a vowel in the alphabet.
____ 9. Choosing a letter E or choosing a letter C in the alphabet.
____ 10. Choosing the month of April or Choosing a summer month in the
Philippines.
Activity 3: Mutually Exclusive or Not?

41. Mutually exclusive
1.Makoy has 60 red chips, 10
yellow chips, and 18 white chips.
What is the probability that
Makoy randomly selects a red
chip or a white chip?
2. A card is drawn from a deck of
cards. What is the probability of
getting a spade or a queen?
NOT MUTUALLY EXCLUSIVE

42. Not Mutually exclusive
events
3. A box contains 15 chips
numbered 1-15. If one chip is
drawn from a box, what is the
probability of getting a number
2 or an even number?

43. ACTIVITY ON MUTUALLY AND NOT MUTUALLY EXCLUSIVE
EVENTS.
A. DETERMINE WHETHER THE SITUATION IS MUTUALLY
EXCLUSIVE(ME) OR NOT MUTUALLY EXCLUSIVE EVENTS
(MI).

44. ACTIVITY ON MUTUALLY AND NOT MUTUALLY EXCLUSIVE
EVENTS.
A. DETERMINE WHETHER THE SITUATION IS MUTUALLY
EXCLUSIVE(ME) OR NOT MUTUALLY EXCLUSIVE EVENTS
(MI).

45. ACTIVITY ON MUTUALLY AND NOT MUTUALLY EXCLUSIVE
EVENTS.
A. DETERMINE WHETHER THE SITUATION IS MUTUALLY
EXCLUSIVE(ME) OR NOT MUTUALLY EXCLUSIVE EVENTS
(MI).

46. ACTIVITY ON MUTUALLY AND NOT MUTUALLY EXCLUSIVE
EVENTS.
B. DETERMINE WHETHER THE SITUATION IS MUTUALLY
EXCLUSIVE(ME) OR NOT MUTUALLY EXCLUSIVE EVENTS
(MI).
1. A restaurant serves a bowl of candies to its customers. The bowl of
candies Gabriel receives has 10 chocolate candies, 8 coffee candies,
and 12 caramel candies. After Gabriel chooses a candy, he eats it. Find
the probability of getting candies with the indicated flavors.
a. P (chocolate or coffee)
b. P (caramel or coffee)
c. P( chocolate or caramel)

47. ACTIVITY ON MUTUALLY AND NOT
MUTUALLY EXCLUSIVE EVENTS.
B. DETERMINE WHETHER THE SITUATION
IS MUTUALLY EXCLUSIVE(ME) OR NOT
MUTUALLY EXCLUSIVE EVENTS (MI).
2. Rhian likes to wear colored shirts. She has 15 shirts
in the closet. Five of these are blue, four shades of
red, and the rest are of different colors. What is the
probability that she will wear a blue or a red shirt?