MathScience Innovation Center Betsey Davis What is Probability? Chance or likelihood of an event...

MathScience Innovation MathScience Innovation Center Center

Betsey DavisBetsey Davis

What is Probability?What is Probability?

Chance or likelihood of an eventChance or likelihood of an event The probability of an event occurring The probability of an event occurring

is equal to the ratio of desired is equal to the ratio of desired outcomes to the total number of outcomes to the total number of possible outcomes (sample space).possible outcomes (sample space).


The probability of an event occurring The probability of an event occurring can be represented as a ratio or the can be represented as a ratio or the equivalent fraction, decimal, or equivalent fraction, decimal, or percent.percent.


A probability of 0 means A probability of 0 means ____________________________________________________

A probability of 1 means A probability of 1 means

________________________________________________________

the event will never occur.the event will never occur.

the event will always occur.the event will always occur.

What is the difference between What is the difference between theoretical and experimental theoretical and experimental

Probability?Probability? Theoretical probability of an event is the Theoretical probability of an event is the

expected probability and can be found with a expected probability and can be found with a formula.formula.

Chances of tossing one coin and getting “heads” is:

1:2 ½ .50 50%

What is the difference between What is the difference between theoretical and experimental theoretical and experimental

Probability?Probability? The experimental probability of an event is The experimental probability of an event is

determined by carrying out a simulation or an determined by carrying out a simulation or an experiment.experiment.

The experimental probability =The experimental probability =

the number of times the desired outcomes occurthe number of times the desired outcomes occur

the number of trials in the experimentthe number of trials in the experiment

What is the Probability of getting What is the Probability of getting “heads” on one coin toss?“heads” on one coin toss?

1 : 21 : 2 ½½ .50.50 50%50%

What is the Probability of getting What is the Probability of getting “red” on one spin?“red” on one spin?

1: 41: 4 1/41/4 .25.25 25 %25 %

What is the Probability of getting What is the Probability of getting “two” on one toss of one die?“two” on one toss of one die?

1: 61: 6 1/61/6 .166666 or .16.166666 or .16 17%17%

What is the What is the Probability Probability of a tossed of a tossed

kiss landing kiss landing upright?upright?

How old are Hershey’s Kisses?How old are Hershey’s Kisses?

Les

s th

an 1

0 ye

ars

Bet

wee

n 10

and 5

0 y.

..

Bet

wee

n 50

and 7

5 y.

..

Ove

r 75

and le

ss th

a...

Ove

r 100

yea

rs

20% 20% 20%20%20%1.1. Less than 10 years Less than 10 years

2.2. Between 10 and 50 yearsBetween 10 and 50 years


4.4. Over 75 and less than 100Over 75 and less than 100

5.5. Over 100 yearsOver 100 years

1010

0of5

How old are Milk Chocolate Kisses?How old are Milk Chocolate Kisses?

Make a predictionMake a prediction

HypothesisHypothesis What is the Probability of the kiss landing flat?What is the Probability of the kiss landing flat? What is the Probability of the kiss landing on a What is the Probability of the kiss landing on a

tilt?tilt? Record your prediction.Record your prediction.

What was your prediction?What was your prediction?The percent of the time I think the The percent of the time I think the

kisses will land flat, x, is:kisses will land flat, x, is: 10

10

% o

r les

s

10%

< x

< 2

0 %

20%

< x

< 3

3.3

%

33.

3% <

x <

50

%

50%

< x

< 6

6.7

%

66.

7% <

x <

75

%

75%

< x

< 1

00 %

14% 14% 14% 14%14%14%14%1.1. 10 % or less10 % or less

2.2. 10% < x 10% < x << 20 % 20 %

3.3. 20% < x 20% < x << 33.3 % 33.3 %

4.4. 33.3% < x 33.3% < x << 50 % 50 %

5.5. 50% < x 50% < x << 66.7 % 66.7 %

6.6. 66.7% < x 66.7% < x << 75 % 75 %

7.7. 75% < x 75% < x << 100 % 100 %

To gather data:To gather data: Work with one partner: 10 kisses totalWork with one partner: 10 kisses total Place all 10 kisses in one cupPlace all 10 kisses in one cup Gently shake cup twiceGently shake cup twice Toss by spilling 2 inches from tabletopToss by spilling 2 inches from tabletop Count flats and tiltsCount flats and tilts RecordRecord Repeat 9 more timesRepeat 9 more times Compute totalCompute total Report your totals to meReport your totals to me

Our Class DataOur Class Data

Our conclusion based on class totalsOur conclusion based on class totals

Why are they named Kisses?Why are they named Kisses?

Are all kisses the same?Are all kisses the same?

Plain: milk chocolatePlain: milk chocolate Dark ChocolateDark Chocolate AlmondAlmond CarmelCarmel

Toss Plain and 2 Other KindsToss Plain and 2 Other Kinds

Milk ChocolateMilk Chocolate Type 1Type 1 Type 2Type 2



How old are Almond Kisses?How old are Almond Kisses?

20%

20%

20%

20%

20%

1.1. Less than 10 years Less than 10 years



4.4. Over 75 and less than 100Over 75 and less than 100

5.5. Over 100 yearsOver 100 years

Mean =

10

0 of 5

How old are Almond Kisses?How old are Almond Kisses?

Published in 2005

Dark Chocolate kisses were added in Dark Chocolate kisses were added in the year:the year:

11 22 33 44 55

10

2003

2001

1997

1993

1985

20% 20% 20%20%20%1.1. 20032003

2.2. 20012001

3.3. 19971997

4.4. 19931993

5.5. 19851985

How old are Dark Chocolate Kisses?How old are Dark Chocolate Kisses?

How many Hershey’s kisses are How many Hershey’s kisses are made each day?made each day?

1.1. 800800

2.2. 80008000

3.3. 80,00080,000

4.4. 800,000800,000

5.5. 8,000,0008,000,000

6.6. 80,000,00080,000,000

7.7. 8,000,000,0008,000,000,000

? Hershey’s Kisses = 1 pound of ? Hershey’s Kisses = 1 pound of chocolate chocolate

6 29 48 62 99

20% 20% 20%20%20%1.1. 66

2.2. 2929

3.3. 4848

4.4. 6262

5.5. 9999

10

0of5

Will different types of kissesWill different types of kisses land on their bases land on their bases

the same percent of the time?the same percent of the time?

Examine your kissesExamine your kisses Notice differencesNotice differences Using what you know about the plain milk Using what you know about the plain milk

chocolate kisses, make predictions for the chocolate kisses, make predictions for the other 2 kindsother 2 kinds

Record your predictionsRecord your predictions

Steps to collect data:Steps to collect data:

Work with one partner: 20 kisses totalWork with one partner: 20 kisses total Place all 20 kisses in one cupPlace all 20 kisses in one cup Gently shake cup twiceGently shake cup twice Toss by spilling 2 inches from tabletopToss by spilling 2 inches from tabletop Count flats of plain and flats of the otherCount flats of plain and flats of the other RecordRecord Repeat 9 more timesRepeat 9 more times Compute totalCompute total Revise your conclusionRevise your conclusion

Move on to page 2:Move on to page 2: Work with one partner: 20 kisses totalWork with one partner: 20 kisses total Place all 20 kisses in one cupPlace all 20 kisses in one cup Gently shake cup twiceGently shake cup twice Toss by spilling 2 inches from tabletopToss by spilling 2 inches from tabletop Count flats of plain and flats of the otherCount flats of plain and flats of the other RecordRecord Repeat 9 more timesRepeat 9 more times Compute totalCompute total Revise your conclusionRevise your conclusion Report results by posting “POST IT” on our stem and leaf and Report results by posting “POST IT” on our stem and leaf and

by reporting to excel.by reporting to excel.

Stem and LeafStem and Leaf

00

11

22

33

44

55

Kiss ablesKiss ables

Advantage:

less expense

Disadvantage:

no paper covering

What percent of What percent of Kissables will land Kissables will land

flat?flat?

17% 17% 17%17%17%17%

1.1. 80%80%

2.2. 66%66%

3.3. 50%50%

4.4. 33%33%

5.5. 25%25%

6.6. 10%10%

11 22 33 44 55

Ever heard of the Kissmobile?Ever heard of the Kissmobile?

MathScience Innovation Center Betsey Davis What is Probability? Chance or likelihood of an event...

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