.

Chapter 3 AP Review

I. In a company, 78% of the employees opt for medical insurance and 42% of theemployees opt for life insurance. 82% of the employees opt for at least one of thesebenefits. What percent of the employees opt for both of these benefits? '\ P{ a-4 \

11/1m../ cOJ. :::rY1 S/l.-y7U'1C e ~ (:( ,4) POf U B).:: P( A) d( Ib/ - t+n h)(A) 4% 1".. -(ZIb) .(B) 18% LLCe Tvt$u.-r<Lt/JU - OSJ. ~ 0,78 +-O?I~ - Y(C) 33% OB;):.:: I,;)., - X-

) 38% -O.?": -}(% 0

I X;, 38\2. Diana has several children and each of her children has several friends, so she can never

be sure how many children will come to dinner. However, over long experience she hasworked out that the probability distribution for the number of children who will cometo dinner is as shown below.

Number of children 0 I 2 3 4 5 6 . 7 8 9 10Probability om 0.04 0.13 0.15 0.16 0.17 0.12 0.09 0.07 0.04 0.02-------------';'

On any given evening, what is the minimum number of places that she should set at thedinner table for the children in order to be at least 80% sure that all the children can beseated? O•.D I j- 0M f. o. 13 -f- (J.tS -I O.lia t-o. n fO.,;;;I -=- (),7g

(~ °7CUU-D D,78 T 0 ,Oq.:.::.JJ , 'f;7 I 56 w, 'the I 6

(C) 8(D) 9(E) 10

3. In a high school there are 638 underclassmen (9th and 10th graders) and 523upperclassmen (11th and 12th graders). Of the underclassmen 83.1% take the bus toschool, and of the upperclassmen 70.9% take the bus to school. If a student is chosen atrandom from those students who tak,e the bus to school, what is the probability that thisstudent is an underclassman? . 3 ~o. e. \.JuS {,38 (. r3,)~5'-36(A) 0.457 '" '$15 D.l5(B) 0.550 , •~,~ ~cc\\0505~~»V"': 17 d(fn If -fa./C{ lPUJ(C) 0.588 v- ~

(D) 0.671 ~.,)J,

(E) 0.831 4.{)~ ~ 0,16,3 -kt!& b£l)

p ( U/llivl cia55 man j -h kt blf~6n Itv' ClQ530 _ 0.58[5

t;~i =371

4. In a random sample of 400 adults, each person stated his or her political preference. Thesex (male/female) of each respondent was also noted. The results are shown in the tablebelow.

18

36

Other78

86

RepublicanMale

Female94881'6

If political preference is indepen nt of sex, which of the following is the expectednumber of respondents who are female. and support the Democratic Party?

(A) 40.04(B) 46.20

~6.45)9~

(E) 103.895

lot? ~- 0-

I 3'1 " 17);). q ,r t'2

uS- A&0

5. When two fair dice are rolled, what is the probability of getting a sum of 7 given thatthe first die rolled is an odd number? A ' dc1 \ _o P(SlLtvl of S€(JUI\ -t=;,s+ UI-f is 0 ) ~ \

~ 'D ( f- $-e.oe-'l ~ -f.l'r~ale oeW j) 5lL vYl () 'f

(B) .1 "p ({,'y51 cUe 15' atlc-J) e: ~J9 w~~

(C) i J- 'tid !3& (1\

(D)r1 80;-(:;,') 0, Lj) (E) i ~()/ ;).~ -=- ~

%>

6. At a certain high school, 1/7 of all s take AP Statistics, 1/4 of all students play.football, and these two events ar in ependent. f a student is chosen at random from .the school, what is the probability at .e student is involved in at least one of these ) (~two pursuits? P (A P 5+0-15 DY ..p.z;otV;a...11):: PCs-fo.f5) +P ( fad '"a t) ~ L 'JI

(A) 7/28 :;;.1. + 1 (J)(.L)(B) 9128 1 4 7 "i

~ 1~;~ (~: Me; . A. .'~I 1lf)IJU" -= I)/14(E) 114 f~~7(A0-A.Li5)

<: PO) , pCp»~

x 2 3 4 5

p(x) 1 2 7 118 9 18 '3

-'

7. Die A has three 2 's, two 1's and one 0 on its faces. Die B has two 2's and four 3's on itsfaces. When either of these dice is rolled, each face has an equal chance of landing ontop. The two dice are tossed. Which of the following represents the probabilitydistribution for the sum of the numbers showing on the two dice?

Q

(B)

(C)

(D)

(E)

x 2 3 4 . 5

p(x) 1 1 1 16' '3 '3 6'

x 2 3 4 5

p(x) 1 1 1 1'4 '4 '4 '4

x 2 3 4 5

p(x) 1 1 7 118 '9 9 18

x 2 3 4 5

p(x) 1 1 7 19 6' 18 '3

l,;? d.. ;;l. I I 0J Lt ~ t+ '3 3 ;;L;;I. Lj It + 3 :3 ~

3 '5 '5 5' if t+ :3'3 S ')- s 4- 4 ,33 ~ )- 5 4 'i ;,~ C; ') is Lj 4 ~

3 -;

8. If a fair coin is tossed five times and comes up heads all five times, then the probabilityof a tail on the sixth toss is

1(A) 32

3(B) 32

(C) Slightlyless than tciD

(E) More than t

-rh.e-~CLv(' llLdt..p"de.YL-f-euLn+5

S() +14 -e pre. 10CLb" It. -fz; LV;' IIflO + c.ho. nqc ./c t'+ (sS+i II I};)

P( 0 _oJ\;) ~p (.:ills)::..

9. Suppose A and B are events with the given probabilities: P(A):= %, and PCB) := !,and

PCB given A) := t. Which of the following conclusions can~ be drawn from the _

given information? P (13) A ) = ~ \. 'PC B IIi)::.. PCB )(A) p(AandB):=iy\L PCB) ~ I);,). / )fl~lldud-

(B) peA or B) := 1 &¥- 'V (A CLN.1 &):: 7>(A ') C PC6)? ~ IZ ::..<J o~