Math 304
Test 2- Probabilitv
Complete as directed (3 pts/problemunlessindicatedotherwise)
L Define"Theoretical
Probabilitv".
-i-k.a
t
S o$
{r^l*Jl.
&
s4.;
e/\)e-.-*
uJiU^
/ J*rt..+
r
\
J
i
{'
r {'yvr-e.u,ijr"
t-).
#{
O r,,^**"f*v--n$
Arv\""
"to
{Z-rf
2. . A coin is tossed5 times.Whatis theprobabilityof gettingat least3 headsamongthe
five flips?Showyourwork.(Hint: applyPascal'sTriangle)
ot-
I
l 3
1 t ub
+
) 1 s l $ 5
f \,
sil 4ts s *
#
" tI
b
33
J
4
af"-
Tossa four-sideddie(1,2,3,4)
3. List thesamplespacefor the followingexperiment:
andthenspina three-colorspinner(Red,White,andBlue)
4f , {w. 1f
4. Is a passwordthat doesnot allow replacement
a permutation?Explain.
of characters
4. Aes
a- ?r+m.
ou-$a-t
",-,/",*.*
LAu-*
nn J{*{s
f €( .
is
a, - o-ira-'^q.
:o.,**- i^-
,,-i|.-JL-'0t-
d +-l*.,-*-lJ +rwa- L,rJi,J./rt*e*-trs",$*^r'*o,t
V
/6
SHORT ANSWER. Write the word or phrase that best completeseachstatementor ansrdersthe question. Show your
work for full credit.(3 pts/problemunlessnoted otherwise)
5) A pair of fair dice is rolled 50 times and the sum of the dots on the faces is noted.
Outcome 12 3
4
5
6
7
8
9
10 11 72
Compute the empirical probability that the sum rolled ir &Euelgg"_2-
a
el-
6) An employment agencyrequired 20 secretarialcandidatesto type the samemanuscript,
The number of errors found in eachmanuscriptis summarizedin the histogram.Find the
empirical probability that a candidatehas lessthan four errors in the typed manuscript.
I
o
d
I
tl
o
tr
6
5
4
1+5
er)
s
2
I.
E
Eonl.
2on3
4onS
Hunben of
6on?
er.r.ons
6)
5
=D"+
, -- L
= fRr = -+/ o
5
nonethan?
7) Constructa possibility tree that shows all possible2-letter codewords using only the
Iettersv, w , x, and y with no repetitions.
\,IW
TD
4i
St
7)
vx
{}
\^J \.1
W K
t\
='t
a
V a-
X
XV
?{w
nt
3v
5v
lettersarepossibleintheword"BASEBALL"?,,
8) Howmanydistinguishablearrangementsof
5O
\O
s)
ffi
4
/44,s{**-o.,
9) A sports shop sold tennis rackets in 2 different weights, 3 types of string and 4 grip sizes.
How many different racketscould be sold?
10) A number cubelabeledwith numbers 1, 2, 3, 4, 5, and 6 is tossed.What are the odds in
favor of the cubeshowing a number lessthan 3?
l:L
10)
&:4 ar
11) Sandysaysthe probabilitythat the arrow will land on 5 or 3 is (1/5) + (1/5) =
11)a.
7t** it ;t is 5-o 3
2lr0
Uus
a. What doesSandyunderstand?b. What doesSandyneed to review?
.
tt<\
n-tsL@l
t*
vvu- s-*
MULTIPLE CHOICE. Choosethe one alternative that best completesthe statementor answersthe question. Show your
work. (2 ptsiprob)
Evaluatethe expression.
' , "t ' {
L-l
12)fr
t
/r
-
dt
V.G
1
) 32
"A' 4
1
D) 42
c) 2!
B)*
z
13) A baseballmanagerhas 1.1playersof the sameability. How many 9 player starting lineups can he
create?
D) 99
c) 362,880
A)ss
u:j.'n0
13)
.r,+,3
ll'Y''1-'g-'L'L
\
?r (t , t tJ , 1, , )/
1.4)There are 5 women running in a race.How many first, second,and third place possibilitiescan
occur?
A) 10
B) 12s
c) 120
-50
A }
E)1s
,.4'3
6
:
m,ETE.|^lcHorcE.
$)--c*
15) tf tre fa{r dtce are rolled, find the probability sf a "double" given that the
sum is 11.
A)+
u)+
c)0
I
16) Given that the od&in favor of a horse winning the race is 4:7 what is the probability that the horse
willwin?
16) €
A)7|lL
B) 7:4
c)7lLo
D) 4lr0
K
E) none of the above
ny
17) Abagcontains 9 red marbles,2 blue marbles,and 5 greenmarbles.What is the probability of
choosinga blue marble?
q
o)u
u)*
,)+,
o)*
SHOIT ANSWXn17. Whatis the prohbility thatyou will hit the shadedregiongiventhat you hit the taryet
somewhere?
Showyour work. 1+pts;
4,.,*; 8'rr , C4n f Jot,l
A + l ^ , ,t.(=a + , 4= t l , r r
--L*s
tf n x. *?"1"r*
17. D,A3
4
Questions18- 20 referto the following: A surveyof how studentget to schoolwas
takenand 140studentsreportedthattheywalk (W) to school,200 studentsreported
thatget a ride (R) to school,75 studentsreportedthey getto schoolmixing how they
walkingandothertimesriding, and25studentsreportedthat they
travelsometimes
neitherwalk nor'dothey geta carride to school(2pts/problem).
18.Sketcha Venndiagramfor theproblem.
P(Wil *1.
19.Calculate
b5 +vt'F*
)7 ts
*,o,ulL
,n.ffi'#
t",
P(Wn R).
20.Calculate
,o.K*#*X ae u
nothing in^y studentswho complainthat
"I'd tike tu dedicatethis day n-a1il
everhaPPmsin school'"
t"iriie