Get out your ISN!
Today’s Objectives:
You will be able to understand the
basic ideas of probability including
outcomes, events, and sample
spaces.
Warm Up
Tape this
into your
Warm Up
Section
and use
the deck
to answer.
WWK & TOC
Choose a colored pencil and
ruler—draw a horizontal line
underneath…
• the last TOC entry (27-28)
• the last WWK entry (Deviation
Standard
)
TOC
29-30 Intro to Probability
WWK
Probability—the chance of an event occurring; 𝑷(𝑬)
Probability Experiment—A chance process that leads
to well-defined results called outcomes.
If you number your WWK…
Outcome—The result of a single trial in a probability
start numbering at 1 again!
experiment
Sample Space—The set of all possible outcomes of a
probability experiment; symbol: 𝑺
more WWK
Event—consists of a set of outcomes of a probability
experiment; symbol: 𝑬
Complement—the set of all outcomes in a sample
space that are NOT included in the event; symbol: 𝑬′
Classical Probability—Uses sample spaces to
determine the probability that an event will happen
Empirical Probability—based on the observations
obtained from an experiment.
Subjective Probability—Uses a probability value based
on an educated guess—approximate information
Big Picture
Unit 3
We are now moving to Unit 3
which is Probability.
The definition of Probability is
the chance that something will
happen—how likely it is that
some event will happen.
Probability
Recall that randomness—randomly
assigning subjects to treatments in
experiments, or randomness in sampling
in observational studies—is a key
component of statistics.
Probability gives us a way to
measure randomness.
First Foldable
Intro to Probability
11/10
Tape Here
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Tape Here
30
Right
Side
Input
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Fold it shut
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nd
2
Fold the
Foldable
in half before taping
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Intro to Probability
30
11/10
Right
Side
Input
Foldable pg. 1
Other Experiments:
•
•
•
Drawing from a deck of cards
Flipping a coin
Drawing a marble from a bag of marbles
Foldable pg. 1
Other Outcomes:
•
•
Drawing from a deck of cards {2 of hearts}
Flipping a coin {T}
heads
heads
tails
tails
heads
tails
FOUR Possible outcomes: HH, HT, TH, TT
Foldable pg. 2
Foldable pg. 2
Foldable pg. 2
𝑺 = {𝑯, 𝑻}
𝑺 = {𝑯𝑯, 𝑯𝑻, 𝑻𝑯, 𝑻𝑻}
More Examples:
•
Three coins are flipped. 𝑆 ={
}
Foldable pg. 3
Other Events:
•
•
Flipping 2 coins and getting 1 tail and 1 head 𝑬 =
{ ?
}
Rolling a die and getting a 1 or a 5 𝑬 ={ ? }
Foldable pg. 3
𝑬 = {𝑯}
heads
heads
tails
tails
heads
𝑺 = {𝑯𝑯𝑯, 𝑯𝑯𝑻,
𝑯𝑻𝑯, 𝑯𝑻𝑻, 𝑻𝑯𝑯,
𝑻𝑯𝑻, 𝑻𝑻𝑯, 𝑻𝑻𝑻}
tails
heads tails heads tails heads tails heads tails
𝑬 = {𝑯𝑯𝑻, 𝑯𝑻𝑯, 𝑻𝑯𝑯}
Foldable pg. 3
Foldable pg. 4
𝑬
𝑺
Foldable pg. 4
𝑬 = 𝑸𝒉, 𝑸𝒄, 𝑸𝒔, 𝑸𝒅 → 𝟒
𝑺 = {𝒘𝒉𝒐𝒍𝒆 𝒅𝒆𝒄𝒌} → 𝟓𝟐
𝑬
𝟒
𝟏
=
=
=. 𝟎𝟕𝟕
𝑺 𝟓𝟐 𝟏𝟑
𝑬 𝟐
= =. 𝟑𝟑
𝑺 𝟔
𝑬 = 𝟏, 𝟑 → 𝟐
𝑺 = {𝟏, 𝟐, 𝟑, 𝟒, 𝟓, 𝟔} → 𝟔
𝑬 𝟑
= =. 𝟓𝟎
𝑺 𝟔
𝑬 = 𝟏, 𝟑, 𝟓 → 𝟑
𝑺 = {𝟏, 𝟐, 𝟑, 𝟒, 𝟓, 𝟔} → 𝟔
You Try!
Foldable pg. 5
𝑬 = 𝟑, 𝟒, 𝟓, 𝟔 → 𝟒
𝟒
𝑷 𝑬 =
𝟔
𝑺 = {𝟏, 𝟐, 𝟑, 𝟒, 𝟓, 𝟔} → 𝟔
𝟔−𝟒 𝟐
𝑷 𝑬′ =
=
𝟔
𝟔
Foldable pg. 5
You Try!
You Try!
You Try!
Foldable pg. 6
Foldable pg. 6
Subjective
Empirical
Classical
Foldable pg. 7
You Try!
Foldable pg. 7
You Try!
You Try!
Tape Here
11/10
Intro to Probability
Tape Here
29
Left
Side
Input
I typed #6 and #7 wrong,
6. “Is #4 a simple of
compound event?”
7. “Is #5 a simple of
compound event?”
Homework
LEFT side