12.4 Probability of Compound Events
Vocabulary
• 12.4 Concurrent Events
–
–
–
–
Compound: two events that are considered together
Overlapping: events with one or more outcomes in common
Disjoint: events with no outcomes in common
Complement: Ā is the complement of A which is all outcomes not
in A
Compound Events
• Compound: two events that are considered
together on one trial
– Overlapping events have one or more outcomes in
common
– Disjoint events have no outcomes in common (often
called mutually exclusive)
• Compound events will generally use the word
‘or’.
(What is the probability of this or that happening
when I …)
Overlapping Events
• Overlapping events have one or more
outcomes in common
– Ex: a number thrown on a fair 6-sided die is < 4 or
it is odd (1 and 3 satisfy both conditions)
– Ex: A card is drawn and it is a number (like 4) or a
suit (like hearts)
Probability of Overlapping Events
• If A and B are two overlapping events, then the
probability of A or B is:
P(A or B) = P(A) + P(B) – P(A and B)
A
B
=
A
+
B
A&B
(Each possibility must be accounted for once and only once)
SAT Test Practice
• A card is randomly selected from a standard
deck of 52 cards. What is the probability that
it is a face card or a spade?
Deck of Cards
Face
card
Spade
Deck of Cards
=
Face
card
Deck of Cards
+
Spade
Deck of Cards
Both
A. ³/₅₂
B. ¹⅟₂₆
C. ²⁵/₅₂
D. ⁷/₁₂
Disjoint Events
• Disjoint events have no outcomes in common
(often called mutually exclusive)
– Ex: A fair 12-sided die is rolled. What is the
probability it will land with a 5 or a 9 up?
– Ex: a disk is drawn from a cup of 5 red, 6 blue, 4
green, and 5 yellow. What is the probability that
the disk is yellow or green?
Probability of Disjoint Events
• If A and B are two disjoint events, then the
probability of A or B is:
P(A or B) = P(A) + P(B)
A
B
=
A
+
B
(Each possibility must be accounted for once and only once)
Find Probability of Disjoint Events
• A card is randomly selected from a standard
deck of 52 cards, What is the probability that
it is a 10 or a face card?
Deck of Cards
10
Face
card
=
Deck of Cards
Deck of Cards
10
Face
card
+
Use a formula to find P(A and B)
• Out of 200 students in a senior class, 113 students are
either varsity athletes or on the honor roll. There are 74
seniors who are varsity athletes and 51 seniors who are on
the honor roll.
– What is the probability that a randomly selected senior is both a
varsity athlete and on the honor roll?
Seniors
Honor
Role
Varsity
Athlete
=
Honor
Role
+
Varsity
Athlete
Both
Try these:
A card is randomly drawn from a standard deck of 52
cards. Find the probability of the given event.
•Selecting an ace or an eight
•Selecting a 10 or a diamond
•In the senior class example, suppose 32 seniors are in
band and 64 seniors are in the band or on the honor roll.
What is the probability that a randomly selected senior is
both in the band and on the honor roll?
Compliments
• Ā is the compliment of A, which is all
outcomes not in A.
Ā
A
A is everything in
the pink circle.
Ā is everything in
the blue region
• The probability of Ā is:
P(Ā) = 1 – P(A)
Find Probabilities of compliments
When two six sided dice are rolled, there are 36
possible outcomes. Find the probability of:
a. The sum is not 6
P(sum not 6) = 1 – P(sum is 6)
b. The sum is less than or equal to 9
P(sum ≤ 9) = 1 –[P(sum is 10)+P(sum is 11)+P(sum is 12)]
Use a Compliment in real life
• A restaurant gives a free fortune cookie to every
guest. The restaurant claims there are 500
different messages hidden inside the fortune
cookies.
– What is the probability that a group of 5 people
receive at least 2 fortune cookies with the same
message?
P(at least 2 fortunes match) = 1 – P(0 matches)
• HW 48: pg 727, 17-27 odd, 28-41 all