Download ppt - Probability of Compound Events Objective: (1) Students will be able to find the probability of a compound event. (2) Students will be able to understand

ProbabilityProbability

of of CompoundCompound

EventsEvents

Probability of Compound Probability of Compound EventsEvents

Objective:Objective:

(1) Students will be able to find the (1) Students will be able to find the probability of a compound event.probability of a compound event.

(2) Students will be able to understand the (2) Students will be able to understand the distinction between simple events and distinction between simple events and compound events.compound events.

Essential Question:Essential Question:

(1) How do I find the probability of a (1) How do I find the probability of a compound event?compound event?

(2) How can I distinguish between a simple (2) How can I distinguish between a simple and compound event?and compound event?


Vocabulary:Vocabulary: OutcomeOutcome – one possible result of a – one possible result of a

probability.probability. Sample SpaceSample Space – the list of possible – the list of possible

outcomes for a probability event.outcomes for a probability event. RandomRandom – outcomes that occur at random if – outcomes that occur at random if

each outcome is equally likely to occur.each outcome is equally likely to occur. Compound EventCompound Event – a specific outcome or – a specific outcome or

type of outcome. type of outcome. Complementary EventsComplementary Events – the events of one – the events of one

outcome happening and that outcomes not outcome happening and that outcomes not happening are complimentary; the sum of the happening are complimentary; the sum of the probabilities of complementary events is 1.probabilities of complementary events is 1.

What is a What is a PROBABILITYPROBABILITY??

- Previously we looked at - Previously we looked at probability for simple probability for simple individual eventsindividual events

- If a simple event involves one, - If a simple event involves one, independent event, compound independent event, compound events include two or more events include two or more simple eventssimple events



number of favorable number of favorable outcomesoutcomes

number of possible number of possible outcomesoutcomes

Examples that use ProbabilityExamples that use Probability::

(1) Dice, (2) Spinners, (3) Coins, (4) (1) Dice, (2) Spinners, (3) Coins, (4) Deck Deck of Cards, (5) Evens/Odds, (6) of Cards, (5) Evens/Odds, (6) Alphabet, Alphabet, Etc.Etc.


P(event) =


0%0% 25% 25% 50% 50% 75% 100% 75% 100%

00 ¼ or .25 ½ 0r .5 ¾ or .75¼ or .25 ½ 0r .5 ¾ or .75 1 1

ImpossibleImpossible Not Very Equally Likely Somewhat Not Very Equally Likely Somewhat CertainCertain

LikelyLikely Likely Likely


Real World ExampleReal World Example::Best Buy is having an IPOD giveaway. They Best Buy is having an IPOD giveaway. They

put all the IPOD Shuffles in a bag. put all the IPOD Shuffles in a bag. Customers may choose an IPOD without Customers may choose an IPOD without looking at the color. Inside the bag are 4 looking at the color. Inside the bag are 4 orange, 5 blue, 6 green, and 5 pink orange, 5 blue, 6 green, and 5 pink IPODS. If Maria chooses one IPOD at IPODS. If Maria chooses one IPOD at random and then her sister chooses one random and then her sister chooses one IPOD at random, what is the probability IPOD at random, what is the probability they will both choose an orange IPOD?they will both choose an orange IPOD?


Real World ExampleReal World Example::Best Buy is having an IPOD giveaway. They Best Buy is having an IPOD giveaway. They

put all the IPOD Shuffles in a bag. put all the IPOD Shuffles in a bag. Customers may choose an IPOD without Customers may choose an IPOD without looking at the color. Inside the bag are 4 looking at the color. Inside the bag are 4 orange, 5 blue, 6 green, and 5 pink orange, 5 blue, 6 green, and 5 pink IPODS. If Maria chooses one IPOD at IPODS. If Maria chooses one IPOD at random and then her sister chooses one random and then her sister chooses one IPOD at random, what is the probability IPOD at random, what is the probability they will both choose an orange IPOD?they will both choose an orange IPOD?

P(orange,orange) =P(orange,orange) = 44//2020 x x 33//1919 = = 33//9595 or 3.2% or 3.2%


What are What are COMPOUND COMPOUND EVENTSEVENTS??

- There are (2) types of - There are (2) types of compound events:compound events:

(1) (1) Independent EventsIndependent Events – involves two – involves two or more events in which the outcome or more events in which the outcome of one event of one event DOES NOTDOES NOT affect the affect the outcome of any other eventsoutcome of any other events

ExamplesExamples:: roll dice, coin flip, problems roll dice, coin flip, problems with replacementwith replacement

P(A and B) = P(A) x P(B)P(A and B) = P(A) x P(B)


What are What are COMPOUND EVENTSCOMPOUND EVENTS??

- There are (2) types of compound - There are (2) types of compound events:events:

(2) (2) Dependent EventsDependent Events - involves two or - involves two or more events in which the outcome of more events in which the outcome of one event one event DOESDOES affect the outcome of affect the outcome of any other eventsany other events

ExamplesExamples:: deck of cards, selecting item deck of cards, selecting item from container, problems without from container, problems without replacementreplacement

P(A and B) = P(A) x P(B following A)P(A and B) = P(A) x P(B following A)


Example 1Example 1:: Roll a dice.Roll a dice.

What is the probability of rolling back What is the probability of rolling back to back sixes?to back sixes?


P(6,then 6) =


What is the probability of rolling back What is the probability of rolling back to back sixes?to back sixes?

11 11 11

66 66 3636


P(6,then 6) = x =

1 1

1 2

1 3

1 4

1 5

1 6

2 1

2 2

2 3

2 4

2 5

2 6

3 1

3 2

3 3

3 4

3 5

3 6

4 1

4 2

4 3

4 4

4 5

4 6

5 1

5 2

5 3

5 4

5 5

5 6

6 1

6 2

6 3

6 4

6 5

6 6


What is the probability of rolling back What is the probability of rolling back to back evens?to back evens?


P(even,then even) =


What is the probability of rolling back What is the probability of rolling back to back evens?to back evens?

33 3 3 9 9 11

66 6 6 36 36 44


P(even,then even) = x = =

1 1

1 2

1 3

1 4

1 5

1 6

2 1

2 2

2 3

2 4

2 5

2 6

3 1

3 2

3 3

3 4

3 5

3 6

4 1

4 2

4 3

4 4

4 5

4 6

5 1

5 2

5 3

5 4

5 5

5 6

6 1

6 2

6 3

6 4

6 5

6 6

Example 3Example 3:: Flip a coin.Flip a coin.

What is the probability of flipping What is the probability of flipping back to back heads?back to back heads?

P(head,then head) =P(head,then head) =


Example 3Example 3:: Flip a coin.Flip a coin.

What is the probability of flipping What is the probability of flipping back to back heads?back to back heads?

Flip 1:Flip 1:

Flip 2:Flip 2:

Outcomes: TT TH HT Outcomes: TT TH HT HHHH

P(head,then head) = ½ x P(head,then head) = ½ x ½ = ¼½ = ¼


Example 4aExample 4a:: Deck of Cards.Deck of Cards.

What is the probability of drawing What is the probability of drawing 2 hearts (without replacement)?2 hearts (without replacement)?

Hint: (1) how many cards are in a deckHint: (1) how many cards are in a deck

(2) how many hearts are in a deck(2) how many hearts are in a deck

(3) if you draw a heart how many card are left(3) if you draw a heart how many card are left

and how many of those cads are heartsand how many of those cads are hearts


Example 4Example 4:: Deck of Cards.Deck of Cards.


Example 4aExample 4a:: Deck of Cards.Deck of Cards.

What is the probability of drawing What is the probability of drawing 2 hearts (without replacement)?2 hearts (without replacement)?

Hint: (1) how many cards are in a deck Hint: (1) how many cards are in a deck (13)(13)

(2) how many hearts are in a deck (2) how many hearts are in a deck (52)(52)


and how many of those cads are hearts and how many of those cads are hearts (12 (12 and 51)and 51)

1313 12 12 11

5252 51 51 1717


P(heart,then heart) = x =

Example 4bExample 4b:: Deck of Cards.Deck of Cards.

What is the probability of drawing What is the probability of drawing 2 hearts (with replacement)?2 hearts (with replacement)?

Hint: (1) how many cards are in a deck Hint: (1) how many cards are in a deck

(2) how many hearts are in a deck (2) how many hearts are in a deck


and how many of those cads are hearts and how many of those cads are hearts


P(heart,then heart) =

Example 4Example 4:: Deck of Cards.Deck of Cards.


Example 4bExample 4b:: Deck of Cards.Deck of Cards.

What is the probability of drawing What is the probability of drawing 2 hearts (with replacement)?2 hearts (with replacement)?

Hint: (1) how many cards are in a deck Hint: (1) how many cards are in a deck (13)(13)

(2) how many hearts are in a deck (2) how many hearts are in a deck (52)(52)


and how many of those cads are hearts and how many of those cads are hearts (13 (13 and 52)and 52)

1313 13 13 11

5252 52 52 1616


P(heart,then heart) = x =

Guided PracticeGuided Practice: : Questions.Questions.

(1) Wyatt has four $1 bills in his wallet and (1) Wyatt has four $1 bills in his wallet and three $10 bills in his wallet. What is the three $10 bills in his wallet. What is the probability he will reach into his wallet twice probability he will reach into his wallet twice and pull out a $10 bill each time? (Assume he and pull out a $10 bill each time? (Assume he does replace the first bill)does replace the first bill)

(2) A bag contains 3 green and 2 purple (2) A bag contains 3 green and 2 purple marbles. What is the probability of drawing marbles. What is the probability of drawing two purple marbles in a row from the bag if two purple marbles in a row from the bag if the first marble is not replaced?the first marble is not replaced?


Guided PracticeGuided Practice: : Answers.Answers.

(1)(1) $1 $1 $1 $1$1 $1 $1 $1 $10 $10 $10$10 $10 $10

33 3 3 99

77 7 7 4949

(2) (2)

P(purple,then purple) = 2/5 x 1/4 = 2/20 = P(purple,then purple) = 2/5 x 1/4 = 2/20 = 1/101/10


P($10,then $10) = x =P($10,then $10) = x =

Independent PracticeIndependent Practice: : Questions.Questions.

(1) Wyatt has four $1 bills in his wallet and (1) Wyatt has four $1 bills in his wallet and three $10 bills in his wallet. What is the three $10 bills in his wallet. What is the probability he will reach into his wallet twice probability he will reach into his wallet twice and pull out a $1 bill each time? (Assume he and pull out a $1 bill each time? (Assume he does not replace the first bill)does not replace the first bill)

(2) A bag contains 3 green and 2 purple (2) A bag contains 3 green and 2 purple marbles. What is the probability of drawing marbles. What is the probability of drawing two green marbles in a row from the bag if two green marbles in a row from the bag if the first marble is replaced?the first marble is replaced?


Independent PracticeIndependent Practice: : Answers.Answers.

(1)(1) $1 $1 $1 $1$1 $1 $1 $1 $10 $10 $10$10 $10 $10

44 3 3 12 12 22

77 6 6 42 42 77

(2) (2)

P(purple,then purple) = 2/5 x 2/5 = P(purple,then purple) = 2/5 x 2/5 = 4/254/25


P($1,then $1) = x = =P($1,then $1) = x = =

SummarySummary: : The difference The difference between simple and compound between simple and compound events:events:

(1) (1) simple eventsimple event – a specific – a specific outcome or type of outcome.outcome or type of outcome.

(2) (2) compound eventcompound event – events – events which consist of two or more which consist of two or more simple events.simple events.


SummarySummary: : The difference between The difference between independent and dependent independent and dependent events:events:

(1) (1) independent eventindependent event – two or more – two or more simple events in which the outcome of simple events in which the outcome of one event one event DOES NOTDOES NOT affect the affect the outcome of other event(s)outcome of other event(s)

(2) (2) dependent eventdependent event – two or more – two or more simple events in which the outcome of simple events in which the outcome of one event one event DOESDOES affect the outcome of affect the outcome of other event(s)other event(s)


Real World ExampleReal World Example::Joanna had 3 roses, 4 tulips, and 1 Joanna had 3 roses, 4 tulips, and 1

carnation in a vase. She randomly carnation in a vase. She randomly selected one flower, took a photo of it, selected one flower, took a photo of it, and put it back. She then repeated the and put it back. She then repeated the steps. What is the probability that she steps. What is the probability that she selected a rose both times?selected a rose both times?

3 3 3 3 99

8 8 8 8 6464


P(rose,then rose) = x P(rose,then rose) = x = =