by Trip Lenahanby Trip Lenahan

2007-2008 2007-2008

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.

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

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

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”

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

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)

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

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

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

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

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

Example of Probability #3Example of Probability #3

ABAB BCBC CDCDACAC BDBDADAD

Probability= 3 = 1

6 2

A

B

C D

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

. . ..

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

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

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