A student takes a 3 question quiz. The probability distribution for the number of questions answered correctly (X) is constructed in a table and histogram. The probability that a student answers at least 2 questions correctly is calculated from the distribution to be 0.375.

1. Name
m*"y#J,_9#1*. ft
ffi Find probabilities of compound eventa.
Vocabulary
The rmion or intersection two eventsis called a compound event.
of
Two eventsareoverlapping ifthey haveone or more outcomesin
common.
Two eventsaredisjoin! or nutually exclusive,if they haveno
outcomes common.
in
ffiAEEE Find probability of disioint events
d card is randomly s€lected from a standard deck of 52 Gards.What is
the probability that it is a 5 or an ace?
Let eventI be selectinga 5 andeventB be selectingan ace.I has4 outcomes
and
B has4 outcomes. Because andB aredisjoint, the probability is:
I
P(A or B) = P(A) + P(B) : 52 ', L : a = sz- n r s a
^ 52 Z 13
mf|sf| Find probability of overlapping events
A card is randomly selected from a standard deck of 52 cards. l,lfhat is
the probability that it is a club or a 3? E
and
Let eventI be selectinga club and eventB be selectinga 3. I has 13 outcomes
. has4 outcomes. these,I outcomeis commonto I andB. fiie probability of
Of
-B =
selecting club ora3 is:
a
PA B): P(A)P(B)P(Aand E + - + : E : fr = o.:os
or + - :
B)
- -
'.4
.=
rcr{rdffifl Use a formula to find PIA and Bl
Given P(Al = o.3, P(8) = O-72' and HA or Et = O.6, find P(A and al' =
E
P(A or B) = P(A) + P(B - P(A nd B write gbneral
formula.
o
0.6: 0.3+ 0.72- P(A and
B) Substituteknown probabilities.
P(A and' : 0.42
B) Solvefor P(l andB). o
.g)
Exercises for Examples 1, 2, and 3
A card is randomly selected from a standard deck of 52 Gards' Find the
probability of the given event.
1. Selectinga queenor a 4 2. Selecting spade a 5
a or
u
3. FindP(,4andB) whenP(l) : 0.25,P(B) : 0.40,andP(A orB) : 0.55.
A|gebra
2
44 ChaoterResource
10 Book

2. i:q1i*n6:1{i?99rit49{6!-r:
l' -
Name Date
PJ"Y#J"
e f- -r'.'i-l F,:i!*"'"'0""0
ffi Find probabilities of oomplements
thereare36 possibleoutcomes'Find the
When two six-sideddice arero11e4
probability of the given went.
a. The sumis lessthan or equalto 3. ,
b. The sumis greaterthan 3.
Solution
a. The outcomes which the sumis lessthan or equalto 3 are
for
(1,r),Q ,1),and(1 , 2 ).
P(sum 3) : 36: i-
< 0'083
b. P(sum>3)= I - P(sum(3)
_ .t l
r_T
1t
12
- 0.917
ffiffi Use a comPlement in real life
I Annual Salary A university conducted nationalresearch
desrees. Fromthe research
a studyofrecipients of PhD
data,the universitydetermined the probability that
that
thie recipientshad annualsalaries of
in excess $95,000 was 0'834' What is the
protaUility that a recipientftom the stuclyhad an annualsalaryof $95,000or less?
E
Solution
The probability that a recipienthad an annualsalaryof $95,000or lessis the
= of
complement oithe went that a recipienthad an annualsalaryin excess $95'000'
: >
P(salary $95,000) I - P(salary $95,000)
<
x
: 1 - 0.834
'..>
a = 0.166
Exercises for ExamPles 4 and 5
=
Find RA).
4. P(A) = 0.63 5. P(l): *
@
6. P('4): o'45 7. P(A):0.0e
8. ln Example5 if the probability that the recipientsof PhD degreeshad annuat
salaries excess
in of$95,000was0.668, whatis theprobabilitythat a recipient
ftom the studyhad an annualsalaryof $95,000or less?
Algebra2
Book
Chapter Resource
10 45

3. Name
W|f.T"y,*,v,
-G,:liA"
s
events'
GEEEI Eiamine independentand dependent
Vocabulary
effect on
Two eventsareindepenilent if the occurrence onehasno
of
the occurrencb the other'
of
ofone
Two events andB are ilependent eventsif the occurrence
I
affectsthe occurrenceofthe other'
is called the
The probabiliWthat B wiil occw giventhatI hasoccurred
A)'
conditionalprobability of B given'4 andis writtenasPB I
f f iFindp r o b a b i | i t y o f t h r e e in d e p e n d e n te ve n ts
of 52 Gards' Each
Kenesha, Sue, and Juan each have a standard deck
card from his or her d€ck. Find the probability that they each
lir*"
draw a " heart.
eventsareindependent'
Let events B, and C be eachpersondrawinga heart'The
l,
so the probabilitYis:
= rrtl
andQ: P (A) ' P ( B ) ' P ( c ) i' i'
P (A ardB i: A : o ' o t t u
I
ffi Find a conditional Probability.
a red card second from a
Find the probability that you randomly select a heart'
si.iaara'ae"f of 52 cards given that the first Gard selected was
Solution
Number of red cards remaining in the deck
P(red cardI heart) : T.rTtal
numberof remainingin the deck
"urds
=fr - o.+eo
Exercises for ExamPles 1 and 2
first
r. e ruir l. tossedtwice. what is the probability of getting a tail on the
"oin
toss,andof gettinga headon the second toss?
that eachtossis a tail'
2. Rich, Amy, and Joeeachtossa coin' Find the probability
second from a
3. Find the probability that you randon y selecta facecard
ae"t of 5i cartli given that tle first cardselectedwas ajack'
stuoaa.a
e
2
Algehra
54 Chapter Book
10Resource
-

4. Name
,a I f'F-l
f,,,*ig#, ",,',,,"0
f;1t)ie
mEEEtrI Gomparilg indeRendentand dependentevents
You randomly select two cards from a standard deck of 52 cards,
Find
the probability that the first card is a diamond and the second card
is
nofa spade if (a) you replace the first card before selecting the second
card, and (bl you do nof replace the first card.
Letl be "the fust cardis a diamond,'andB
be..thesecond
cardis nol a spade.,,
a. With replacement, probability of drawinga diamond,andthen
the
zot drawinga spadeis:
p(A B) p(A). :
and= p(B')
E. # : i. i :ft - o.raa
b. Without replacement, probability of drawinga diamond,and
the
thenro, dmwinga spade is:
p (AandB): p(Bl: g.#:
p(A).
i .#: ffi - o.rso
Hf.fitl{rfi Solve a multi-step problem
FocusTesting A companyfocustestsa nev/proteinbar.The focus grotp ts 52o/o
male. Of the malesin the group60% saidthat they would buy the protein bar, and of
the females,460lo that they would buy the proteinbar Find the probability that a
said
randomlyselected personwould buy the proteinbar.
Solution
A probabilitiy tree diagramcanhelp you solvethe problem.Notice that the
E
probabilitiesfor all branches
from the samepoint must sumto 1.
Event C: will buy bar
EventD: will not buy bar
Event C: will buy bar
'6
Event D: will not buy bar
P(will buy proteinbar) : P(A and C) + P(B andA
6
: P(A).P(clA) p@). {clB)
+
'o
: (0.s2X0.60)
+ (0.48X0.46)
- 0.533
@
Exercises for Examples 3 and 4
Find the probability of drawing the given cards from a standard deck of
52 cards (a) with replacement and (b) without replacement.
4. A heart,then a club 5. A nine, then a three
6, In Example4, find the probability that a personwould buy the protein bar, if
78%ofthe malesand82%ofthe females theywouldbuy theproteinbar.
said
,n.0,.,
ror.,filnili"ri
55

5. Name
aE 91"y,..9,v-.F,,*1$.
ru Studyprobabilitydistributions.
Vocabulary
A random variable is a variablewhosevalue is determined the
by
outcomes a randomevent.
of
A probability distribution is a f,rnctionthat givesthe probability of
eachpossiblevalue of a randomvariable.
A binomial distribution shows probabilities
the ofthe outcomes a
of
binomial experiment.
A binomial experimenthasn independent trials, hasonly two
oulcomes(success failure) for eachtrial, andthe probability for
or
success thesame each
is for trial-
A probability distribution symmetricifa verticalline canbe drawn
is
to dividethe histogram two partsthataremirror images.
into
A distribution that is not symmetricis called skewed.
f{.f{|lEf Gonstruct a probab i I ity distri bution
I Let Xbe a random variable that represents the number of questions
that students answered correctly on a quiz with three questions. Make
a table and a histogram showing the probability distlibution for X,
E Thepossible valuesofXare theintegers0,1,2,and3. Thetableshows numberof
the
.s possibleoutcomes P(X).
and
E
.2
.=
=
En4Writ.:fllnterpret a probability distribution
@
Use the probability distribution in Example 1 to find the probability
.9
that a student enswers a! leas! twe qrestiens correctly.
The probability that a student answersat least tvo questions correctly is:
P(x>z): P(x:2) + P(x: 3)
_?1Ll
= ; * 8 : g : t:o s
Algebra2
Chapter Besource
10 Book 65
---

6. Name
f;;;ie' " a
[TbrlP-."y,*,y" ",'t,,
Exercises for Examples 1 and 2
1. Use the datato constructa probability distributiontable and a histogram
showingthe probability distribution for X, a randomvariablethat represents
the numberof cell phones household.
per
2. What is the probability that a household at leasttwo cell phones?
has
ruWnm Constructa binomialdistribution
A binomial experiment consists of n = 3 trials
with probability O.4 of buccess on €ach tria!.
Draw a histogram of the binomial distribution
that shows the probability of exactly k successes.
p(k: o) : 0.216
- 3co(0.4)o(0.6)3
P(k: 1): 3C{0.4)t(0.6)2 :0.432
:
P(k : 2): 3c2(0.4)2(0.o10.288
: o.oo+
P(k: 3): .q10.+f1o.o1o
rulHttll Interpret and classify a binomial 4istribution
E
a. What is the leastlikely outcomefor the binomial distribution rn
.E
Example 3?
b. What is the probability when ft : 1 in Example3?
c. Describethe shapeof the binomial distributionin Example3.
Solution -
.9
a. The leastlikely outcomeis the valueofft for which P(ft) is
smallest. This probdbility is smallestfor /c: 3. =
b. Theprobability whent : I is 0.432.
=
c- The distributionis skewed because is not symmetricaboutany
it 6
vertical line. o
Exercises for Examples 3 and 4 @
ln Excic:se3 3-5 ..:eethe fo!!cur!.9 infcrmelien. -l- binonria! expeiiment
consists of n = 4 trials with probability o.1 of success on each trial.
3. Constructa binomial distributionthat showsthe probability of exactlyft
successes drawa histogramof the distribution.
and
4- Find the most likely outcome.
5. Describethe shaoe the binomial distribution.
of
Algebra
2
ChapterResource
10 Book