Quiz 10-3 You have the following bills in your wallet: three $20’s, four $10’s, five $5’s, and...

Quiz 10-3Quiz 10-3You have the following bills in your wallet: three $20’s, four $10’s, five $5’s, and six $1’s. What is the number of You have the following bills in your wallet: three $20’s, four $10’s, five $5’s, and six $1’s. What is the number of distinct ways distinct ways you could pay out the bills one at a time?you could pay out the bills one at a time?

1. 1.

!6!*5!*4!*3

!18 080,594,514

!!*!*

!

CBA

N

2. 2. How many distinct license plates can be made using How many distinct license plates can be made using 2 digits (numerals 0 – 9) and 4 letters ( a – z) ?2 digits (numerals 0 – 9) and 4 letters ( a – z) ? # # L L L L# # L L L L 26*26*26*26*10*10 600,697,45

3. 3. What is the probability of getting 4 aces in a randomly dealt hand of 4 What is the probability of getting 4 aces in a randomly dealt hand of 4 cards?cards?

452

44

C

C 0000037.0

725,270

1

10-410-4

Disjoint and Overlapping EventsDisjoint and Overlapping Events

Theoretical ProbabilityTheoretical Probability

outcomes possible of # total

event that achieve to waysof #)( eventP

bag in the marbles of # total

bag in the marbles red of #)( redP

The probability of an event occurring: The probability of an event occurring:

There are 4 different colored marbles in a bag (red, blue, greenThere are 4 different colored marbles in a bag (red, blue, green and clear). What is the probability of pulling out a red oneand clear). What is the probability of pulling out a red one on the first try?on the first try?

25.04

1)( redP

VocabularyVocabularycompound eventscompound events: more than one : more than one event occurring.event occurring.

picking picking 2 red 2 red ANDAND 1 green1 green..

picking picking 2 red 2 red OROR 1 green1 green..

Is there difference between Is there difference between OR OR and and AND AND ??

Which has the higher probability, Which has the higher probability, OR OR and and AND AND ??

5 red5 red, , 4 blue4 blue, , 3 3 green green

Bag of marblesBag of marbles

“ “Disjoint eventsDisjoint events: (mutually exclusive). The chance of one : (mutually exclusive). The chance of one event does not affect the chance of another event. event does not affect the chance of another event.

Event #1Event #1: : picking a picking a red marblered marble from the first bag and from the first bag and

Event #2Event #2 picking a picking a green marble green marble from the second bag.from the second bag.

4 red4 red, , 3 green 3 green

Bag #2Bag #2


Bag #1Bag #1

“ “Disjoint eventsDisjoint events: (mutually exclusive). The chance of one : (mutually exclusive). The chance of one event does not affect the chance of another event. event does not affect the chance of another event.

Event #1Event #1: : picking a picking a red marblered marble from the bag from the bag

Event #2Event #2 replacing the replacing the red marblered marble then picking a then picking a green green marble marble from the bag.from the bag.



5

2)( redP

5

3)( greenP

“ “Overlapping eventsOverlapping events: (not mutually exclusive). The chance : (not mutually exclusive). The chance of one event is affected by the preceding event. of one event is affected by the preceding event.

Event #1Event #1: : picking a picking a red marblered marble from the bag from the bag

Event #2Event #2 without replacing the without replacing the red marble,red marble, picking a picking a green marble green marble from the bag.from the bag.



5

2)( redP

4

3)( greenP

Venn DiagramsVenn DiagramsGroup AGroup A Group B

Disjoint events: they Disjoint events: they have nothing in commonhave nothing in common.

Elements of group A (only): Elements of group A (only):

Number of elements in group A: Number of elements in group A: 44

Elements of group B (only): Elements of group B (only):

Number of elements in group B: Number of elements in group B: 22

Total Number of elements in groups A and B: Total Number of elements in groups A and B: 66

Probability of Probability of disjointdisjoint events. events.

BlackHair

RedRedHairHair

3 44

““disjoint” (events don’t overlap)disjoint” (events don’t overlap)

17

4

7

3 hair) redor black ( P

P(A or B) = P(A) + P(B)P(A or B) = P(A) + P(B)

Your turn:Your turn:There are 20 people in an English class. Five are German, 12 are Mexican, and 3 are Italians. What is the probability of being either Mexican or There are 20 people in an English class. Five are German, 12 are Mexican, and 3 are Italians. What is the probability of being either Mexican or Italian if you are in this class?Italian if you are in this class?

1. 1.

2. 2. What is the probability of dealing either a King or a What is the probability of dealing either a King or a Queen from a deck of cards if you deal one card only?Queen from a deck of cards if you deal one card only?

152

14

152

14

C

C

C

C

20

3

20

12

20

15 75.0

4

3

52

4

52

4 154.0

13

2

Venn DiagramsVenn DiagramsGroup BGroup BGroup A

Overlapping events: they Overlapping events: they have something in commonhave something in common.

Elements in group AElements in group A

Elements in group B Elements in group B

Elements in group A or BElements in group A or B

Elements in A: Elements in A: 44

Elements in B: Elements in B: 44

Elements in both Elements in both A and B: A and B: 66

Why can’t you add the number in A and the number in B Why can’t you add the number in A and the number in B to get the total number of elements?to get the total number of elements?

Double-counting the overlap!Double-counting the overlap!

Total number = (# in A) + (# in B) – (# in overlap)Total number = (# in A) + (# in B) – (# in overlap)

Probability of Probability of overlappingoverlapping events. events.

BlondeBlondeHairHair

GirlsBill Jim

? girl)or blond( P

Amber MariaAngelica

5

1

5

3

5

3 girl)or blond( P

P(blond or Girl) = P(blond) + P(girl) – P(blond and girl)P(blond or Girl) = P(blond) + P(girl) – P(blond and girl)

P(A or B)= P(A) + P(B) – P(overlap)P(A or B)= P(A) + P(B) – P(overlap)

5

5

P(A or B) = P(A) + P(B) – P(A and B)P(A or B) = P(A) + P(B) – P(A and B)

Total number = (# in A) + (# in B) – (# in overlap)Total number = (# in A) + (# in B) – (# in overlap)


Hearts Face cards

Hearts: J, Q, K

total number of cards = ?total number of cards = ?

A, 2,3,4,5,6,7,8,9,10

Spades: J, Q, K Clubs: J, Q, K

Diamonds: J,Q,K

# hearts = ?# hearts = ?

# face cards = ?# face cards = ? # hearts and face cards = ?# hearts and face cards = ?

?heart)( P

?card) face andheart ( P

22

25

22

12

22

13) FCor H( P

?card) face( P

Probability > 1Probability > 1 the universe just “imploded”the universe just “imploded”

22

12

22

3

= 13= 13 = 22= 22

= 12= 12 = 3= 3

22

13

22

3

22

12

22

13) FCor H( P

P(A or B) = P(A) + P(B) – P(A and B)P(A or B) = P(A) + P(B) – P(A and B)

22

22


HeartsFace cards

Hearts: J, Q, K

A, 2,3,4,5,6,7,8,9,10

Spades: J, Q, K Clubs: J, Q, K

Diamonds: J,Q,K

22

13heart)( P

22

3card) face andheart ( P

22

12card) face( P

What does “OR” mean? What does “OR” mean?

““OR”: one of the two conditions is met, OR”: one of the two conditions is met, NOT BOTH NOT BOTH conditions.conditions.

We need to subtract out the probability of both conditions occurring.We need to subtract out the probability of both conditions occurring.

FC) and P(H - P(FC) P(H)FC)or H( P

22

3 -

22

12

22

13FC)or H( P 1FC)or H( P

Probability of Probability of disjointdisjoint or or overlappingoverlapping events.events.

““disjointdisjoint” (mutually exclusive):” (mutually exclusive):

)(P(A) B)or ( BPAP

““overlappingoverlapping””

B) and ()(P(A) B)or ( APBPAP

Using the formulas:Using the formulas:

P(A) = 0.5 P(A) = 0.5 P(B) = 0.35P(B) = 0.35

““disjointdisjoint” (mutually exclusive):” (mutually exclusive): )(P(A) B)or ( BPAP ““overlappingoverlapping”” B) and ()(P(A) B)or ( APBPAP

P(A and B) = 0.2P(A and B) = 0.2

P(A or B) = ?P(A or B) = ? B) and ()(P(A) B)or ( APBPAP 2.035.05.0B)or ( AP 65.0

P(A) = 0.2P(A) = 0.2 P(B) = 0.6P(B) = 0.6 P(A or B) = 0.7P(A or B) = 0.7

P(A and B) = ?P(A and B) = ? B) and ()(P(A) B)or ( APBPAP

) and (6.02.07.0 BAP7.06.02.0B) and ( AP

Solve for P(A and B) Solve for P(A and B)

1.0B) and ( AP

Your turn:Your turn:

P(A) = 0.8 P(A) = 0.8 P(B) = 0.25P(B) = 0.25

““overlappingoverlapping”” B) and ()(P(A) B)or ( APBPAP

P(A and B) = 0.1P(A and B) = 0.1

P(A or B) = ?P(A or B) = ? B) and ()(P(A) B)or ( APBPAP

1.025.08.0B)or ( AP 95.0P(A) = 0.37P(A) = 0.37 P(B) = 0.49P(B) = 0.49 P(A or B) = 0.65P(A or B) = 0.65

P(A and B) = ?P(A and B) = ? B) and ()(P(A) B)or ( APBPAP ) and (49.037.065.0 BAP

65.049.037.0B) and ( AP

Solve for P(A and B) Solve for P(A and B)

21.0B) and ( AP

3. 3.

4. 4.

Theoretical ProbabilityTheoretical Probability



bag theofout letters 3 thedraw to waysof # total

C then B,A, draw to waysof #),,( CBAP

The probability of an event occurring: The probability of an event occurring:

The challenge you have is The challenge you have is countingcounting the ways that define success the ways that define success and then counting the total possible outcomes.and then counting the total possible outcomes.

3!

1

What is the probility of pulling an What is the probility of pulling an AA, followed by a , followed by a BB, and then, and then aa C C out of a bag with the letters ‘A’, ‘B’, and ‘C’ in it ?out of a bag with the letters ‘A’, ‘B’, and ‘C’ in it ?

3 permutate 3

3 choose 3),,( CBAP 61.0

6

1

Your Turn:Your Turn:5. 5. What is the probality of being dealt a 5 card hand that What is the probality of being dealt a 5 card hand that

has 3 kings and 2 Aces?has 3 kings and 2 Aces?

6. 6. What is the probability of picking 1 red or a green marble What is the probability of picking 1 red or a green marble from a bag containing 2 red and 3 green marbles? from a bag containing 2 red and 3 green marbles?



7. 7. In a room of people, there are 15 boys and 17 girls. 5 of In a room of people, there are 15 boys and 17 girls. 5 of the boys have blond hair and 4 or the girls have blond the boys have blond hair and 4 or the girls have blond hair. What is the probability of having blond hair? hair. What is the probability of having blond hair?

8. 8. In a room of people, there are 20 boys and 18 girls. 8 of In a room of people, there are 20 boys and 18 girls. 8 of the boys have black hair and 4 or the girls have black the boys have black hair and 4 or the girls have black hair. What is the probability of not having black hair and hair. What is the probability of not having black hair and being a boy?being a boy?

Geometric ProbabilityGeometric Probability

25

75

125

9. 9. What is the probability of hitting the pink ring? What is the probability of hitting the pink ring?

10. 10. What is the probability of hitting either the pink or dark blue ring? What is the probability of hitting either the pink or dark blue ring?

11. 11. What is the probability of not hitting the pink ring? What is the probability of not hitting the pink ring?

Your Turn:Your Turn:

12. 12. At the Roy High School Talent show 7 musicians are scheduled to At the Roy High School Talent show 7 musicians are scheduled to perform. They are: Bill, Brad, Bob, and Brody (boys) and Kylee, perform. They are: Bill, Brad, Bob, and Brody (boys) and Kylee, Kaylee, and Kyla (3 girls). What is the probability that 2 boys will be Kaylee, and Kyla (3 girls). What is the probability that 2 boys will be first? first?



orderin people 7) (of 2 arrange to waysof #

orderin boys 4 of 2 arrange toways#)1 boys 2( st P

2 choose 7

2 choose 4)1 boys 2( st P

27

24

C

C 29.0

21

6


13. 13. What is the probability of getting 3 aces in a randomly dealt hand of 7 What is the probability of getting 3 aces in a randomly dealt hand of 7 cards?cards?



52. ofout cards 7get to waysof #

cards 4out aces 3get toways#)aces 4( P

7 choose 52

3 choose 4)acesr ( P

752

34

C

C 30 000 000.0

560,784,133

4


14. 14. The lottery uses numbers 1 thru 46. 6 numbers are drawn randomly. The lottery uses numbers 1 thru 46. 6 numbers are drawn randomly. The order in which you choose the numbers doesn’t matter. What is The order in which you choose the numbers doesn’t matter. What is the probability of winning the lottery if you buy one ticket (assume the probability of winning the lottery if you buy one ticket (assume nobody else picks the winning number) ? nobody else picks the winning number) ?



numbers 46 of 6pick to waysof #

numberscorrect 6 get the toways#)'# 6( sP

6 choose 46

6 choose 6)w( inP

646

1

C 00000011.0

819,366,9

1

How many ways can you get the 6 out of 6 correct numbers? How many ways can you get the 6 out of 6 correct numbers?

How many ways can you pick 6 of 46 numbers?How many ways can you pick 6 of 46 numbers?

Is picking 6 of 46 a permutation or a combination?Is picking 6 of 46 a permutation or a combination?

The probability of something The probability of something NOTNOT happening.happening.

The probability that it will rain is 50%. The probability that it will rain is 50%.

What is the probability that it What is the probability that it won’twon’t rain? rain?

The probability that it will rain is 20%. The probability that it will rain is 20%.

What is the probability that it What is the probability that it won’twon’t rain? rain?

%50)( rainP%50%100)( niarP

%20)( rainP

%20%100)( niarP

)(AP Means: “the probability that event A will Means: “the probability that event A will not happennot happen..

Probability for the Sum of Two Fair Probability for the Sum of Two Fair DiceDice

Die Roll 11 22 33 44 55 66

11 22 33 44 55 66 77

22 33 44 55 66 77 88

33 44 55 66 77 88 99

44 55 66 77 88 99 1010

55 66 77 88 99 1010 1111

66 77 88 99 1010 1111 1212

SumsSums

SumsSums

rollspossibleoftotal

agettowayseP

......#..

7........#..)(

61.06

1

36

6)( eP

Using Venn Diagrams:Using Venn Diagrams:

In a parking lot, In a parking lot, 60% of the cars are Fords 60% of the cars are Fords and the rest are of other makes. and the rest are of other makes. 30% of 30% of the Fords are whitethe Fords are white. . 50% of all the cars are white. 50% of all the cars are white.

Fords: 0.6White

Cars: 0.5White Fords0.18

1.0 - 0.42 - 0.18 – 0.32 = 0.08

What percentage of the cars that are not Fords are not white?What percentage of the cars that are not Fords are not white?

Other non-Ford,non-white cars

Fords (not white)

0.6*0.7 =0.42

White non-fords:

0.5 – 0.18 =0.32

8%8%

If a car were chosen randomly, what is the probability that it is notIf a car were chosen randomly, what is the probability that it is not a ford and is white?a ford and is white?

32%32%

% of cars that are white fords = 0.3 * 0.6 = 0.18 % of cars that are white fords = 0.3 * 0.6 = 0.18

Quiz 10-3 You have the following bills in your wallet: three $20’s, four $10’s, five $5’s, and...

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Transcript of Quiz 10-3 You have the following bills in your wallet: three $20’s, four $10’s, five $5’s, and...