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12.1/12.2 Probability
Quick Vocab:
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Random experiment: “random” act, no way of
knowing ahead of time
Outcome: results of a random experiment
Event: a set of outcomes
Sample space: the set ALL possible
outcomes
Probability
“Probability of an event”
P(Event) = P(E)
# of outcomes in the event

# of total outcomes in the sample space
Toss of coin:
Probability of landing on heads:
1
P(H) =
2
Probability
P(will definitely occur) = 1
ex: Have 1 die P(roll a #) = 1
P(never occur) = 0
ex: Have 1 die P(roll a letter) = 0
Probability
Two dice are rolled and the numbers are noted. Find
the probability of each event.
a) The sum of the numbers is less than 5
Sum < 5 ?
Possibilities when 2 dice are rolled
(Pg. 632 in book)
TOTAL = 36
Probability
Two dice are rolled and the numbers are noted. Find
the probability of each event.
a) The sum of the numbers is less than 5
6 1
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36 6
b)
The sum of the numbers is 4 or 5.
Sum = 4 or 5 ?
Possibilities when 2 dice are rolled
Probability
Two dice are rolled and the numbers are noted. Find
the probability of each event.
a) The sum of the numbers is less than 5
6 1

36 6
b)
The sum of the numbers is 4 or 5.
P(4 or 5) =
7
36
Standard Deck of Cards
Clubs Hearts Diamonds Spades
(Black) (Red)
(Red)
(Black)
52 cards in the deck
26 black, 26 red
4 suits: hearts, diamonds, clubs, spades
13 of each suit
Face cards: Have a FACE!! (not Ace)
A card is drawn from a standard
deck of 52 cards.
What is the probability that the following occurs?
P( a red card)
26 26  1
52 2
# of red cards in deck?

P(a spade)
# of s in deck?
13
13
1

52
4
A card is drawn from a standard
deck of 52 cards.
What is the probability that the following occurs?
TOO: P(the card is a heart)
# of s in deck? 13
13 1
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52 4
8
2
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52 13
P(the card is a 3 or 4)
# of 3s? 4
# of 4s? 4
A card is drawn from a standard
deck of 52 cards.
What is the probability that the following occurs?
TOO: P(between a 2 and 5, inclusive)
# of each ? 4
2, 3, 4, and 5: 4 x 4=16
16 4
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52 13
A nickel, dime and quarter are
flipped. H=heads, T=tails
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How many elements are in the sample
space? 8
HHH, HHT, HTH, THH, TTH, THT, HTT, TTT
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Find P(exactly 2 tails) 3
8
P(nickel or dime are heads)
HHH, HHT, HTH, THH, TTH, THT, HTT, TTT
6 3
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8 4
A nickel, dime and quarter are
flipped. H=heads, T=tails
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TOO: Find P(at least 2 tails) 4
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P(4 heads) 0
0
8
1
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8 2
HHH, HHT, HTH, THH, TTH, THT, HTT, TTT
Homework
Pg. 633 #1-13, Pg. 635-636 Q1-10, 1 & 2