Probability - Greer Middle College || Building the Future

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

Tape Here

Tape Here

30

Right Side Input

Tape Here

Tape Here

Fold it shut Tape Here

nd 2

Fold the Foldable in half before taping

Tape Here

Tape Here

Tape Here

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