This is Paper Test # 6 [Go to web quiz 6]
Numerical answers are in our text, Rolf ;
Methods will be discussed using other problems.
Links to other web pages were not on original test;
Caution : Prof McFarland creates new tests each semester |
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Mathematics 143 |
Test 6 (hour exam) |
given Spring 2008 |
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Your
final
finite
fantasy
VI
____
game
image |
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__________________
PRINT name above |
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grade on this test |
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__________________
credit on web quiz #6 |
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[A] Except possibly for [1] and [2], put answers and work in blue books
[B] Credit given in proportion to the clarity of your WORK
[C] You need not repeat work in one problem already displayed in another
[D] Except in [1c] below, you may write answers using the symbols n!, P(n,r), C(n,r) |
| [1] |
(a)(1 pt)(Pg 474 part of #43)(1 pt) Write C(8,3) as an integer (it is between 50 and 100); show work, not just calculator output.
For all other problems on this test, you may leave
"C(n,k)" un-evaluated. |
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(b)(Pg 506 #1h)(2 pts) Four rappers have nick-names S,
L, D, J. List all duets (such as
{S, L} )
which can be chosen from this set of 4 people. |
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(c)(2 pts)(take-home test, #3 on website link) On the Venn diagram (right),
shade in the set
A'  (BC)' |
| [2] |
(Pg 439 #35, #23c,d) A survey of 145
students revealed that last month::
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77 spoke French |
28 spoke French and a Malay |
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65 spoke Malay |
25 spoke French and Polish |
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61 spoke Polish |
18 spoke Malay and Polish |
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7 spoke all three languages |
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(a)(3 pts) Place numbers in appropriate parts of the Venn
diagram above interpreting the given information.
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(b)(1 pt) How many tourists spoke none of these languages? |
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In the above Venn diagram,
F = set of tourists who spoke French,
M = set of tourists who spoke Malay,
P = set of tourists who spoke Polish |
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(c)(1 pt) How many tourists spoke exactly one of these languages? |
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| [3] |
(a)(1 pt)(Pg 450 #53) In how many different ways can 4 Americans and 3
Iraqis be seated in a row if no person sits next to a person of the same
nationality? |
E
H |
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(b)(2 pts)(Pg 482 #3) KLM Airlines is giving away 3 identical free
tickets. Seven students at UWW apply to win a ticket. How many trios of ticket
winners are possible? |
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(c)(2 pts)(#35 Pg 460) How many different 4-letter "words" can be formed from
the letters of the word COMPUTER? (a "word" need not have meaning ;
examples are CUTE, TOUR, and CTRM) |
| [4] |
(a)(1 pt)(Pg 436 #5) Given n(A) = 15, n(B) = 22, and n(A  B) = 30,
find n(A B). |
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(b)(2 pts)(part of #39 Pg 460) In how many ways can Hannah seat 5 of her 11
students in a row? |
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(c)(2 pts)(P 474 #43) Three novels are chosen from a reading list of 8 novels.
How many such trios are there? |
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(a)(1 pts)(Pg 516 #15) What is the probability of at least one head
appearing on two tosses of a coin? |
E
H |
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(b)(2 pts)(Pg 482 part of #7) In how many different ways can a
110-member senior class name a president, vice-president, and secretary? |
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(c)(2 pts)(Pg 529 #27) In a group of 35 aliens from the planet Z#kkoops,
10 have purple hair, 14 have yellow eyes, and 4 have both purple hair and yellow
eyes. What is the probability that a randomly selected alien will have either
purple hair or yellow eyes or both? (show work) |
| [6] |
(a)(1 pt)(Pg 542 #11) If P(E) = 0.6 , P(F) = 0.7 , and P(E F) = 0.3,
find P(F|E). |
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(b)(2 pts)(Pg 542 #15) Prof McFarland puts two problems
(A and B) on a test. The probability that a student solves A
is 0.75 ; the probability that a student solves B is
0.45 ; and the probability that a student solves both is
0.20. Kyle solves B. What is the probablity that Kyle also
solves A ? |
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(c)(2 pts)(Pg 543 #25) The local Ameritech motor pool contains 6 Chevies
and 8 Fords. Don and Hanika are randonly assigned one car each. What is the
probability that both are assigned Chevies? |
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(a)(Pg 561 #23b)(1 pt) If E and F are independent events, and P(E) = 0.2 and
P(F) = 0.6 , find P(E F) . |
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(b)(2 pts)(Pg 560 #19a) The probability that Jake comes to class on a
warm spring day is 0.2 ; the probability that Brenda comes to class on such a day
is 0.3 . Jake and Brenda do not know each other.
What is the probability that neither of these persons shows up on the same warm spring day? |
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(c)(2 pts)(Pg 562 #35) A card is drawn from a normal 52-card deck. Let E
be event that the card is red, and let F be the event that the card is a face
card. First (for 1 point) find P(E F). Then (for
another point) decide whether or not E and F are independent by checking the appropriate box below : |
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P(E)= |
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; P(F)= |
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; P(E F)= |
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; Check one box at right : |
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Independent |
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; Dependent |
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(Pg 577 #33) In an earlier year, the Senate contained 55 Republicans and 45
Democrats. Bill #301 was supported by 20% of the Republicans and 80% of the Democrats.
Senator Snort supported Bill #301 ; what is the probability that Senator
Snort was a Republican ? |
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(a)(1 pt) Define in English events E and F so that the answer
to the underlined question above is P(E | F). |
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(b)(2 pts) Using set and probability symbols, but using NO
ENGLISH WORDS, interpret the numbers 55 , 80% , and 20% in the
problem. Thus, you might (incorrectly) write
P(E'F) = 0.80 |
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(c)(2 pts) Find P(E | F), i.e., find the probability that
Senator Snort was a Republican. |
| [9] |
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(Pg 624 #41) Laurie is a waitress at the Athens Club. Eighty percent (80%)
of her customers leave a tip of 15% or more. |
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(a)(3 pts) What is the probability that exactly 4 of Laurie's 6 customers will
leave a tip of 15% or more? |
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(b)(2 pts) What is the probability that at least 4 of Laurie's 6 customers will
leave a tip of 15% or more? |
Note that the text problem (Pg 678 #41) above asked about "4 customers" but did not specify
whether this meant "exactly 4" or "at least 4". Both interpretations are
asked above, with different answers. Both types of questions appear in
the text and on web quiz 6.
Note that the text problem (Pg 678 #41) above asked about "4 customers" but did not specify
whether this meant "exactly 4" or "at least 4".
Both interpretations
are asked above (and on web quiz #6), with different answers. |
