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SCORE: /34 NAME; A a .. W:
Math 151 A03 & A04 Assignment #1 DUE: ,' ‘FKJDAY FEBRUARYSJ‘I‘ 2010
At the START 0t CLASS — NO EXCEPTIONS! ANSWERS ALONE WILL EARN YOU NO CREDIT.
ALL RELEVANT WORKINGS MUST BE SHOWN IN FULL. COMPLETE EACH QUESTION AS IF YOU WERE PRESENTING YOUR SOLUTION
IN THE CONTEXT of an EXAM. ['2'] 1. How many licence plates can I create if each plate is made up of three letters followed
by three digits with the added condition that the letters can only be As, Bs, Cs, Ds or
Es, and the three numbers have to be arranged in increasing order and must be selected
from {0, 1, 2, 3, 4, 5, 6, 7}. Repetition is allowed where the letters are concerned but _ . .. f A i "
not where the diglts are concerned. CTW’E. swamU a a w Jr». t at!
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[3 2. Ten students are chosen at random from a group of eighteen of which Bettina,
Alphonso and Germaine are a part. What is the probability that Bettina, Alphonso
and Germaine are all among the Chosen? (3m: titti .< r' w 4;, 3: r‘ t a it" i
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[3] 3. Six musical instruments are available for loan. Assuming all are loaned, in how many different ways can these be assigned to the four musicians in the graduate music
ensemble such that each instrument is loaned to one musician, each musician gets at least one instrument and no musician has more than {Lexingtmments on man? 5; a n tauLLLL [3] 4. A survey of 100 Victoria residents revealed that 59 regularly read The Times Colonist, 24
regularly read The Globe and Mail, 40 regularly read Monday Magazine, 12 regularly
read both The Times Colonist and The Globe & Mail, 22 regularly read both The Times
Colonist and Monday Magazine, 60 regularly read The Globe & Mail or Monday
Magazine (or both), and 87 regularly read at least one of these three newspapers. How
many residents in the survey regularly read only the Times Colonist? A completed Venn Diagram must be included as part of yOur answer.
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['21 5 If a sixcard hand is dealt from a well—shuffled standard deck of 52 playing cards, what
is the probability that the hand contains two pairs (Le. two cards of one rank, two cards of
a second rank, one card of a third rank, and one card of a fourth rank)? Give your
answer as a decimal rounded to two decimal places.
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[6] 6. Given Q, R and S as independent events in a given experiment complete the following
formulae by filling in the blanks:
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V) HQCm 5) z i I} ‘ vi) Qw(Pm S) = V ' r H t v“ 'P (if e W ,3 2 [3'1 15] I have ten distinct textbooks to arrange on my bookshelf. Four of them are mathematics
textbooks and I'd like to arrange the books in such a way that at least two of the
mathematics textbooks are adjacent to one another. How many different such arrangements are possible? I r
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"Spin—and—Win" is under new management. The new
management has created the spinner to the right and now
charges $1 per spin. (The person spinning wins the 
amount pointed to by the Spinner.) $2.00 Cost: $1 per spin a) What is the expected value for this game? [3] . “D” I
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#11 I l: ' ’ ' 6 I b) What does your answer in part 'a' mean for the ownerfmanager, if there are 1000 customers who play the game in a week? [2i 4: dex c / fit/armam .._r, c 1 v.) : L [7l Team Math and Team English are competing in an ‘intellectual challenge’. In order to
win the contest a team must be victorious in a ‘best of three’ scenario in other
words the winning team needs to win two games in total. The first two tests involve a
lot of formulae and therefore the probability of Team Math emerging victorious on the
first test is .8 and the probability of Team English emerging victorious on the second
test is .2. The third test, however, requires a fair bit of essay writing so the probability
of Team English coming out on top in that test is .7. a) \k‘. b) What is the probability that the intellectual challenge is decided before the
third test is even started? [3] e ’ \ "' I” * \ ’ x ?’ “Kl ‘ f
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Answer should be given correct to three decimal places. [2] \ .. \ fp{ N? m’ > 2.2:: A/i’A/i } _ awr s x “A
Jr , . What is the probability that Team English wins the challenge?
Answer should be given correct to three decimal places. [2] .c #7 l! r" ...
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 Spring '09
 Barone
 Math

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