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W Homework 5 Fall 2008 Math 3122 Anderson
KW. Name:
1. Suppose the sample space is
Q : {01,02,03904,'0)5,605} , v
where ' R efgé “3‘ ‘W%%W§l§
13(01):.2 1‘ sq Let =
A = {02,c04,a)6} EVA w$ ‘%wv\ﬁe§
B = {01,604,605ﬂiéh ' mete, m a Q“
C={a)1,a)6} m "
Find 3; ?€@m%\% m“
@ a; P(A[B): “2:, :3 “gym 3% x
W%\ :1;
b, P(BfA): % «a W a ﬁ
$4 “3 "g; “x , .\
W3? 0 “Alan—m: e. WE‘elmEe e a?
do P2 8 = ea c; 2°?Cife mﬁ‘xw ﬁ’ ..
< l > R 4 W 0%
e. P(B]A): £3 a @kﬁ new 1 ﬂaw
u” “even 5 2. A woman"s clothing'store owner, buys from three compames: A, B, and C. The most recent ‘
purchases are shown here  . ‘ Company A Company B 1 CompanyC .
Dresses 24 18' ' U 12 g LE
' Blouses ‘13 f 36 '_ J 1.5 ' lg Eel
Pants 36 y 14 12 e “2;
“We w ﬁg ﬂ v? Q An item from the} store is seleoled at random. Flind'the priob‘ability the iterh ls' ’
a,‘ made by Company A? WQ ' 2 . W]
b made by Company A g1ven 1t was a blouse? “@(5 ﬁsm @ QR \ \e\oW¢\ “‘5 9% He made by Corhpany A and it was a blouse ? ‘? i. seem? % Wm W \ga‘bﬁg
be. d. made by Compahy Al‘or it was a blouse? "? K (Am ‘Qﬁ \} ‘o‘w “X. W” l \‘8 e
\U‘ 3": given made'by Company A; it was a blouse? “W \e‘wm \ Egng %\ a» ﬁlglaﬁ
 f not made by Company A given it was a blouse? K? k“ @W‘Q egg \ \,®\,€W\
‘W
" ' r ’ . 7 WW A 3. An urn contains 6 red, 3 green, and 7 white balls. Two balls are selected at random without replacement one at a time
a What is the probability that the second is red given the first was red? viga‘tﬁm “'3 % b. What is the probability that the second was red given the ﬁrst was not red? s ~ v = “stamina e 4%
_ c. What is the. probability the second ball was red? ates?“ % 4‘ Shoes come in two types, biggies and tinies. Forty percent of shoes are biggies and sixty percent
are tiniest Of biggie shoes 20% are too small for. their oWner “and 15% of thetinies are to large for their owners. Bigie shoes can only be too small for their owner and2 tinies can only be too big for
their owners. Suppose a pair of shoes do not'ﬁt its owner, 'what is the probability the pair is a
biggie? 4,“? ggaa g§%}n ﬁmle' V
@ ' i . ' " I; \x n 3%
Wit \@\ amt e: \ N‘s» kﬁi a, E 5. Box 1 contains 4 red and 6 green balls, Box? contains 6 red and 9 green balls, and BOX 3 contains
3 red and 5 green balls A box is chosen at random, and two balls are selected without replacament. Draw a tree diagram ' ' gag, (33%th %W
a. What is the probability that the are
1. Both red? 2% g % @i use {3:}
‘ i ’  ' \ é % “3 at
h 93A ii. One red and the other éh‘iﬁt? m ‘9 % 1N ® \S’\
Q er ' V t :g g\ at; 335% \e s “ %§ %
\ $5” I it h white? Egg Q2 (Cg. b. If both balls are red, what is the probability that the balls were drawn from i. ~ I m L Box 17 ﬁﬁﬁws \ \ \@§§\§°[email protected]\ % B ?  , _ . i ‘ ' ‘11,VOX2 ’1 H ~ =§%&§ , ﬁa§% \ _ Box 3? WWVBMi \\§e% gmﬁh at: 6‘ An um contains 6 red and 4 green balls. A ball is selected at random, if it is red, we place it back in
the um and add 5 more red balls. Ifthe ball was green we replace it in the urn and add 5 more
green ball. Two more balls are then selected from the urn without replacement. a. What is the probability that the last two balls selected are green? ?( £§\v3\\ 2. ’?({%m \EA VCRN a ?( (ﬁt9 \‘R‘z\ '?&‘R‘2§
.. “at g A "m A a V \% $0 I“? s “a”
6% i “iii? 02‘) m
b. What is the probability that the last two balls selected are the same color as the first ball
selected?  apt)“ M {WW .2. rec Nﬁﬂﬂn?u§;\ s... ‘W taxea‘ii‘aﬁ‘VCGA ’\°( \m 1. mm :(‘§_\b°a¥ (il \ an; ‘45 \Q . V\‘5\) i9
A 7 7. The probability that an employee at a company is female is .36. a. The probability that the person is married given the person is female is Find the probability
that the person is female and is married. ?( E “ mm\‘ 3N b. In addition it is known that the probability a randomly selected employee is married is .58, I1, v i. Find the’probability of a randomly selected employee is male.
T’ \M\ “is ﬁe“
(a
0 ii. Find the probability that a randomly selected employee is unmarried given the employee is
male. (Hint: You will ﬁnd it useful to create a table.)
A? “m m \ mu‘i '1 R “ES; Qg\{§sm wk ﬁvyﬂg ‘a 0 9‘8 ﬁxwﬁ queh @K ﬁg“ §$%\ ﬁ‘ﬁ‘b‘wé‘kx calm MR“ gs» \wwﬂvﬁ u\% %““§\ QRVXVk @‘yKQm W ?K \§\\‘ Xﬁx “ w\%v‘§\qﬁa ﬁQV \;«}\ \mw‘gx
we. <\%R(n%\ “a. a ma, \%‘a\\~sw \~m~\ .V’Mk' Wk &m% MW \géka am ...
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 Spring '10
 ANDERSON
 Probability, Probability theory, Randomness, green balls, randomly selected employee, tinies

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