vocabulary 12.4 concurrent events – compound: two events that are considered together –...
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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
12.4 Probability of Compound Events
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)
= + -
(Each possibility must be accounted for once and only once)
A B
A & B
A B
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?
= + -
A. ³/₅₂ B. ¹⅟₂₆ C. ²⁵/₅₂ D. ⁷/₁₂
SpadeFace card
Face card Spade
Both
Deck of Cards Deck of Cards Deck of Cards Deck of Cards
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)
= +
(Each possibility must be accounted for once and only once)
A B A B
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?
= +10
Face card 10
Face card
Deck of Cards Deck of CardsDeck of Cards
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?
= + -Varsity Athlete
Honor Role
Honor Role
Varsity Athlete
Both
Seniors
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.
• The probability of Ā is: P(Ā) = 1 – P(A)
AĀ A is everything in
the pink circle.
Ā is everything in the blue region
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
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