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This pdf teaches how we can calculate the probability of some of the simple events and what vocabulary is used for calculating the probability of any random event.

1.
of Simple

Events

Events

2.
Probability of Simple Events

Life is full of random events!

You need to get a "feel" for

them to be a smart and

successful person.

The toss of a coin, throw of a

dice and lottery draws are all

examples of random events.

Life is full of random events!

You need to get a "feel" for

them to be a smart and

successful person.

The toss of a coin, throw of a

dice and lottery draws are all

examples of random events.

3.
Probability of Simple Events

Students will be able to find the probability of a

simple event.

Students will be able to understand the

distinction between simple events and

compound events.

Essential Question:

(1) How do I find the probability of a simple

event?

(2) How can I distinguish between a simple and

compound event?

Students will be able to find the probability of a

simple event.

Students will be able to understand the

distinction between simple events and

compound events.

Essential Question:

(1) How do I find the probability of a simple

event?

(2) How can I distinguish between a simple and

compound event?

4.
Probability of Simple Events

Vocabulary: Some words have special meaning in

Probability

Experiment or Trial: an action where the result is

uncertain.

Outcome: one possible result of an experiment.

Simple Event: a specific outcome, just one of the

possible outcomes.

Sample Space: the list of possible outcomes

Random: outcomes that occur at random if each

outcome is equally likely to occur.

Complementary Events: the events of one outcome

happening (E) and that outcomes not happening

( not E) are complimentary or opposite; the sum of

the probabilities of complementary events is 1.

Vocabulary: Some words have special meaning in

Probability

Experiment or Trial: an action where the result is

uncertain.

Outcome: one possible result of an experiment.

Simple Event: a specific outcome, just one of the

possible outcomes.

Sample Space: the list of possible outcomes

Random: outcomes that occur at random if each

outcome is equally likely to occur.

Complementary Events: the events of one outcome

happening (E) and that outcomes not happening

( not E) are complimentary or opposite; the sum of

the probabilities of complementary events is 1.

5.
Probability of Simple Events

Probability is the measure of the

likelihood that an event will occur

Probability does not tell us exactly what will

happen, it is just a guide

It is the ratio of

number of favorable outcomes

to the

total number of possible outcomes

Probability is the measure of the

likelihood that an event will occur

Probability does not tell us exactly what will

happen, it is just a guide

It is the ratio of

number of favorable outcomes

to the

total number of possible outcomes

6.
CLASSICAL PROBABILITY

number of favorable outcomes

P(Event) = number of possible outcomes

Two Hypothesis :

Equally likely outcomes and Finished outcomes

Property

The probability is a number between 0 and 1

The probability of the certain event is 1

The probability of the impossible event is 0

in symbols:

number of favorable outcomes

P(Event) = number of possible outcomes

Two Hypothesis :

Equally likely outcomes and Finished outcomes

Property

The probability is a number between 0 and 1

The probability of the certain event is 1

The probability of the impossible event is 0

in symbols:

7.
Classical PROBABILITY

The probability of an Event can be

as a FRACTION : 1/4

as Unitary PERCENTAGE

between 0 and 1 : 0.25

as a PERCENTAGE

between 0% to 100% : 25%

The probability of an Event can be

as a FRACTION : 1/4

as Unitary PERCENTAGE

between 0 and 1 : 0.25

as a PERCENTAGE

between 0% to 100% : 25%

8.
Probability of Simple Events

PROBABILITY LINE

0% 25% 50% 75% 100%

0 ¼ or .25 ½ 0r .5 ¾ or .75 1

Impossible Not Very Equally Likely Somewhat Certain

Likely Likely

PROBABILITY LINE

0% 25% 50% 75% 100%

0 ¼ or .25 ½ 0r .5 ¾ or .75 1

Impossible Not Very Equally Likely Somewhat Certain

Likely Likely

9.
Examples

that use Probability

1) Flip a Coin,

2) Roll a Dice,

3) Spinners

4) Pick a card from a deck of 52 Cards

5) Choose at ramdom a ball from a box

that use Probability

1) Flip a Coin,

2) Roll a Dice,

3) Spinners

4) Pick a card from a deck of 52 Cards

5) Choose at ramdom a ball from a box

10.
Probability of Simple Events

Example 1: Flip a coin - Tossing a Coin

What is the probability of flipping a tail?

When a coin is tossed, there are two possible outcomes:

head (H) or tail (T)

P(event ) = # favorable outcomes

# possible outcomes

1 1

P(tail) = =

2 2

The probability is 1 out of 2 or .5 or 50%

Also… the probability of flipping a HEAD is ½.

Example 1: Flip a coin - Tossing a Coin

What is the probability of flipping a tail?

When a coin is tossed, there are two possible outcomes:

head (H) or tail (T)

P(event ) = # favorable outcomes

# possible outcomes

1 1

P(tail) = =

2 2

The probability is 1 out of 2 or .5 or 50%

Also… the probability of flipping a HEAD is ½.

11.
TREE

Example 1

DIAGRAMM - FLIP A COIN

the sample space of events can be represented by

a tree diagram:

There are two

"branches" (Head and Tail)

The probability of each branch

is written on the branch

head tail

The outcome is written at the

end of the branch

Notes: the SUM of the probabilities

of the individual events is ONE ( Total Probability )

Example 1

DIAGRAMM - FLIP A COIN

the sample space of events can be represented by

a tree diagram:

There are two

"branches" (Head and Tail)

The probability of each branch

is written on the branch

head tail

The outcome is written at the

end of the branch

Notes: the SUM of the probabilities

of the individual events is ONE ( Total Probability )

12.
Here is a tree diagram for the toss

of a coin:

of a coin:

13.
Probability of Simple Events

Example 2: Roll a dice - Throwing Dice

a) What is the probability of rolling a 4 ?

# favorable outcomes

P(event) =

# possible outcomes

1

P(rolling a 4) =

6

The probability of rolling a 4 is 1 out of 6

When a single dice is thrown, there are six possible outcomes

The probability of any one of them is 1/6 !

Example 2: Roll a dice - Throwing Dice

a) What is the probability of rolling a 4 ?

# favorable outcomes

P(event) =

# possible outcomes

1

P(rolling a 4) =

6

The probability of rolling a 4 is 1 out of 6

When a single dice is thrown, there are six possible outcomes

The probability of any one of them is 1/6 !

14.
Example 2: Roll a dice.

b) What is the probability of rolling an even

number? ( or an odd number)

P(event) = # favorable outcomes

# possible outcomes

3 1

P(even #) = =

6 2

The probability of rolling an even number ( or an odd

number ) is 3 out of 6 or .5 or 50%

b) What is the probability of rolling an even

number? ( or an odd number)

P(event) = # favorable outcomes

# possible outcomes

3 1

P(even #) = =

6 2

The probability of rolling an even number ( or an odd

number ) is 3 out of 6 or .5 or 50%

15.
TREE DIAGRAMM

ROLL A DICE

on the branches

you must write

the probability

Notes: the SUM of the probabilities

of the individual events is 1 ( Total Probability)

ROLL A DICE

on the branches

you must write

the probability

Notes: the SUM of the probabilities

of the individual events is 1 ( Total Probability)

16.
Spinners

Example 3:.

What is the probability of spinning green?

P(event) = # favorable outcomes

# possible outcomes

1 1

P(green) = =

4 4

The probability of spinning green is 1 out of 4

or .25 or 25%

Example 3:.

What is the probability of spinning green?

P(event) = # favorable outcomes

# possible outcomes

1 1

P(green) = =

4 4

The probability of spinning green is 1 out of 4

or .25 or 25%

17.
Pick a card from a Deck of

Example 4: 52 Cards

A deck of 52 cards includes thirteen ranks of

each of the four suits :

hearts (♥) , diamonds (♦) spades (♠) and clubs (♣)

Each suit has 10 numbered cards

and 3 figures : jack, queen and king.

Example 4: 52 Cards

A deck of 52 cards includes thirteen ranks of

each of the four suits :

hearts (♥) , diamonds (♦) spades (♠) and clubs (♣)

Each suit has 10 numbered cards

and 3 figures : jack, queen and king.

18.
Pick a card from a Deck of

Example 4

52 Cards

What is the probability of picking a heart?

# favorable outcomes 13 1

P(heart) = = =

# possible outcomes 52 4

The probability of picking a heart is

1 out of 4 or .25 or 25%

What is the probability of picking a not heart?

# favorable outcomes 39 3

P(nonheart) = = =

# possible outcomes 52 4

3 out of 4 or .75 or 75%

“heart” and “Not heart” are complementary (opposite) events !

P(notE) = 1- P(E)

Example 4

52 Cards

What is the probability of picking a heart?

# favorable outcomes 13 1

P(heart) = = =

# possible outcomes 52 4

The probability of picking a heart is

1 out of 4 or .25 or 25%

What is the probability of picking a not heart?

# favorable outcomes 39 3

P(nonheart) = = =

# possible outcomes 52 4

3 out of 4 or .75 or 75%

“heart” and “Not heart” are complementary (opposite) events !

P(notE) = 1- P(E)

19.
Choose at random a

ball from the box

Example 5:

A box contains 5 red balls, 3 green balls and 2

yellow balls. What is the probability of :

a) choose at random a green ball?

# favorable outcomes 3

P(green) = =

# possible outcomes = 10

3 out of 10 or .3 or 30%

b) choose at random a red ball?

# favorable outcomes 5

P(red) = =

# possible outcomes 10 or .5 or 50%

ball from the box

Example 5:

A box contains 5 red balls, 3 green balls and 2

yellow balls. What is the probability of :

a) choose at random a green ball?

# favorable outcomes 3

P(green) = =

# possible outcomes = 10

3 out of 10 or .3 or 30%

b) choose at random a red ball?

# favorable outcomes 5

P(red) = =

# possible outcomes 10 or .5 or 50%

20.
Example 5: TREE DIAGRAMM

Chose at random a ball from the bag

Red Green Yellow

notes: the SUM of the probabilities of the

individual events is ONE (Total Probability)

Chose at random a ball from the bag

Red Green Yellow

notes: the SUM of the probabilities of the

individual events is ONE (Total Probability)