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by Trip Lenahan by Trip Lenahan 2007-2008 2007-2008

By Trip Lenahan by Trip Lenahan2007-2008. What is Probability? ► Probability is the likelihood of something happening. ► Probability is expressed as a

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Page 1: By Trip Lenahan by Trip Lenahan2007-2008. What is Probability? ► Probability is the likelihood of something happening. ► Probability is expressed as a

by Trip Lenahanby Trip Lenahan

2007-2008 2007-2008

Page 2: By Trip Lenahan by Trip Lenahan2007-2008. What is Probability? ► Probability is the likelihood of something happening. ► Probability is expressed as a

What is Probability?What is Probability?

►Probability is the likelihood of Probability is the likelihood of something happening.something happening.

►Probability is expressed as a fraction Probability is expressed as a fraction as the number of desired outcomes as the number of desired outcomes over the number of possible outcomes.over the number of possible outcomes.

Page 3: By Trip Lenahan by Trip Lenahan2007-2008. What is Probability? ► Probability is the likelihood of something happening. ► Probability is expressed as a

ProbabilityProbability

►The highest probability of an event The highest probability of an event occurring is:occurring is:

11

►The lowest probability of an event The lowest probability of an event occurring is:occurring is:

00

Page 4: By Trip Lenahan by Trip Lenahan2007-2008. What is Probability? ► Probability is the likelihood of something happening. ► Probability is expressed as a

Professions That Use Professions That Use ProbabilityProbability

► Insurance companiesInsurance companies► Professional card playersProfessional card players► Casino operatorsCasino operators► AthletesAthletes► Sports AnalystsSports Analysts► Statistics keepersStatistics keepers► SecretariesSecretaries► AccountantsAccountants►DoctorsDoctors

Page 5: By Trip Lenahan by Trip Lenahan2007-2008. What is Probability? ► Probability is the likelihood of something happening. ► Probability is expressed as a

Two-Step ProcedureTwo-Step Procedure

To determine probability, one may use To determine probability, one may use this two-step procedure:this two-step procedure:

1. Determine and count all logical 1. Determine and count all logical possibilitiespossibilities

2. Determine and count all desired 2. Determine and count all desired possibilities or “winners”possibilities or “winners”

Page 6: By Trip Lenahan by Trip Lenahan2007-2008. What is Probability? ► Probability is the likelihood of something happening. ► Probability is expressed as a

Probability FormulaProbability Formula

The Probability Formulas are as follows:The Probability Formulas are as follows:

p= number of winnersp= number of winners total number of possibilitiestotal number of possibilities

OROR p= winning regionp= winning region

total possible regiontotal possible region

Page 7: By Trip Lenahan by Trip Lenahan2007-2008. What is Probability? ► Probability is the likelihood of something happening. ► Probability is expressed as a

Example of Probability #1Example of Probability #1

► If there are 10 balls (7 red, 3 green) then If there are 10 balls (7 red, 3 green) then the likelihood of selecting a red ball on one the likelihood of selecting a red ball on one attempt is ….attempt is ….

7 7 red balls (winners)red balls (winners)

10 10 total balls (total total balls (total possibilities)possibilities)

Page 8: By Trip Lenahan by Trip Lenahan2007-2008. What is Probability? ► Probability is the likelihood of something happening. ► Probability is expressed as a

Example of Probability #2Example of Probability #2

ProblemProblem:: If one of the four points is picked If one of the four points is picked randomly, what is the probability that the randomly, what is the probability that the point lies on CA?point lies on CA?

A

B

C D

Page 9: By Trip Lenahan by Trip Lenahan2007-2008. What is Probability? ► Probability is the likelihood of something happening. ► Probability is expressed as a

Example of Probability #2 Example of Probability #2 (cont)(cont)

►To solve this problem, we first list allTo solve this problem, we first list all

possibilitiespossibilities

AA BB CC DD►Then, we circle the winnersThen, we circle the winners

AA BB CC DDA

B

C D

Page 10: By Trip Lenahan by Trip Lenahan2007-2008. What is Probability? ► Probability is the likelihood of something happening. ► Probability is expressed as a

Example of Probability #2 Example of Probability #2 SolutionSolution

Therefore the probability of the selected Therefore the probability of the selected point being on the angle is: point being on the angle is:

Winners = Winners = 33

Possibilities Possibilities 44

Page 11: By Trip Lenahan by Trip Lenahan2007-2008. What is Probability? ► Probability is the likelihood of something happening. ► Probability is expressed as a

Practice Problem #1Practice Problem #1

If one of the four angles is selected If one of the four angles is selected randomly, what is the probability that randomly, what is the probability that

the angle is acute?the angle is acute? A. ¼ B. ½ C. ¾ D. 1

Page 12: By Trip Lenahan by Trip Lenahan2007-2008. What is Probability? ► Probability is the likelihood of something happening. ► Probability is expressed as a

Example of Probability #3Example of Probability #3

ProblemProblem:: If If twotwo of the four points are of the four points are picked at random, what is the probability picked at random, what is the probability that both lie on CA?that both lie on CA?

A

B

C D

Page 13: By Trip Lenahan by Trip Lenahan2007-2008. What is Probability? ► Probability is the likelihood of something happening. ► Probability is expressed as a

Example of Probability #3Example of Probability #3

ABAB BCBC CDCDACAC BDBDADAD

Probability= 3 = 1

6 2

A

B

C D

Page 14: By Trip Lenahan by Trip Lenahan2007-2008. What is Probability? ► Probability is the likelihood of something happening. ► Probability is expressed as a

More Probability More Probability (pg 52 #10)(pg 52 #10)

If point B is chosen on AC, what is the If point B is chosen on AC, what is the probability that -5 < B < 7?probability that -5 < B < 7?

A C

-20 10-5 7

A. 2/5 B. 12/10 C. 1/15 D. 3/5

. . ..

Page 15: By Trip Lenahan by Trip Lenahan2007-2008. What is Probability? ► Probability is the likelihood of something happening. ► Probability is expressed as a

Still more… Still more… (pg 52 #11)(pg 52 #11)

The second hand of a clock sweeps The second hand of a clock sweeps continuously around the face of the clock. continuously around the face of the clock.

What is the probability that at any What is the probability that at any random moment the second hand is random moment the second hand is

between 7 and 12?between 7 and 12?

A. 7/12 B. 7/60 C. 12/60 D. 5/12

Page 16: By Trip Lenahan by Trip Lenahan2007-2008. What is Probability? ► Probability is the likelihood of something happening. ► Probability is expressed as a

Last one… Last one… (pg 52 #15)(pg 52 #15)

If a point is chosen at random in If a point is chosen at random in rectangle ABCD, what is the rectangle ABCD, what is the

probability that:probability that:

a. It is in square SQUA?a. It is in square SQUA?

A. 2/9 B. 1/5

C. 3/5 D. 1/3

9

2

35

CB

A D

S Q

U

Page 17: By Trip Lenahan by Trip Lenahan2007-2008. What is Probability? ► Probability is the likelihood of something happening. ► Probability is expressed as a

Last one (really)… Last one (really)… (pg 52 #15)(pg 52 #15)

If a point is chosen at random in If a point is chosen at random in rectangle ABCD, what is the rectangle ABCD, what is the

probability that:probability that:

b. It is b. It is notnot in square SQUA? in square SQUA?

A. 2/5 B. 1/5

C. 3/5 D. 4/5

9

2

35

CB

A D

S Q

U