Section 5.2 Completed Notes

1

Foranyrandomphenomenon,eachtrialhasanoutcomeandanycollectionofoutcomesisanevent.

1)For8lippingtwo-coinsoutcomes:

events:

2)Fortherandomphenomenon,rollingtwodiceoutcomes:

events:

FormalProbability

Aprobabilitymodelisamathematicaldescriptionofarandomphenomenonconsistingoftwoparts:

1.Asamplespace,S,containingallpossibleoutcomes.

2.Awayofassigningprobabilitiestoevents.

NOTATION:WedenotetheprobabilityofaneventasP(event)

Section 5.2 Completed Notes

2

ProbabilityRules(KNOWTHESE!)

1.Anyprobabilityisanumberbetween0and1(inclusive)

TheprobabilityP(A)ofanyeventAsatis8ies

2.Allpossibleoutcomestogethermusthaveprobability1.

IfSisthesamplespaceinaprobabilitymodel,thenP(S)=1

3.Theprobabilitythataneventdoesoccuris1minustheprobabilitythattheeventdoesnotoccur(itscomplement)

ForanyeventA,

4.Iftwoeventshavenooutcomesincommon,theprobabilitythatoneortheotheroccursisthesumoftheirindividualprobabilities.

TwoeventsAandBaredisjointiftheyhavenooutcomesincommonandsocanneveroccursimultaneously.IfAandBaredisjoint,

Section 5.2 Completed Notes

3

Acompanythatofferscoursestopreparewould-beMBAstudentsfortheGraduateManagementAdmissionTest(GMAT)hasthefollowinginformationaboutitscustomers:20%arecurrentlyundergraduatestudentsinbusiness;15%areundergraduatestudentsinother8ieldsofstudy;60%arecollegegraduateswhoarecurrentlyemployed;and5%arecollegegraduateswhoarenotemployed.

(a)Isthisalegitimateassignmentofprobabilitiestocustomerbackgrounds?Why?

(b)Whatpercentofcustomersarecurrentlyundergraduates?

(a)Whatprobabilityshouldreplace"?"inthedistribution?

(b)WhatistheprobabilitythataCanadian'smothertongueisnotEnglish?

Canadahastwoof8iciallanguages,EnglishandFrench.ChooseaCanadianatrandomandask,"Whatisyourmothertongue?"Hereisthedistributionofresponses,combiningmanyseparatelanguagesfromthebroadAsian/Paci8icregion:

Section 5.2 Completed Notes

4

Suppose there are 100 random US residents and 18 have traveled to Canada, 9 have traveled to Mexico, and 4 have traveled to both countries.

Are the events traveling to Canada and traveling to Mexico disjoint?

Find the probability that a randomly chosen American has traveled to either Canada or Mexico.

If we draw a Venn Diagram representing two non-disjoint events, A and B, we can come up with our rule for addition when two events are not disjoint.

This is called the General Addition Rule.

Section 5.2 Completed Notes

5

A study of the students taking distance learning courses at a university find that they are mostly older students not living in the university town. Choose a distance-learning student at random. Let A be the event that the student is 25 years old or older and B the event that the student is local. The study finds that P(A) = 0.7, P(B) = 0.25, and P(A and B) = 0.05.

(a) What is the probability that the student is less than 25 years old?

(b) What is the probability that the student is at least 25 years old and not local?

(c) What is the probability that the student is at least 25 years old or local?

Section 5.2 Completed Notes

6

Employment data at a large company reveal that 72% of the workers are married, that 44% are college graduates, and that 23% are married college graduates. What's the probability that a randomly chosen worker...

(a) is neither married nor a college graduate?

(b) is married but not a college graduate?

(c) is married or a college graduate?

Musical styles other than rock and pop are becoming more popular. A survey of college students finds that 38% like country music, 24% like gospel music, 11% like rap music, 5% like gospel and country music, 8% like rap and country music, 4% like rap and gospel music, and 1% like all three.

(a) Make a Venn diagram with these results.

(b) What percent of college students like country but not gospel?

(c) What percent like none of these?

(d) What percent like gospel and rap but not country?

Section 5.2 Completed Notes

7

Wecanalsousetwo-waytablestodetermineprobabilities.Here are the counts (in thousands) of earned degrees in the United States in the 2001-2002 academic year, classified by level and by the sex of the degree recipient:

(a) What is the probability of a degree recipient earning a doctorate and being female?

(b) What is the probability of being female?

(c) What is the probability of being a doctorate degree recipient?

(d) What is the probability of being female or a doctorate degree recipeint?

Homework:p.309#s27,29,31-36all,43-55odd