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MATH 110 EXAM tt3A|l^l I NAME MAY 5, 1997 % J SECTION
SHOW ALL WORK TO GET FULL CREDIT.
- List the elements in each set
[2] (a) The set of all outcomes of tossing a coin and a six-sided die.
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[3] (b) The set of all outcomes of tossing two six-sided dice such that the numbers add to 7 or 11.
2. Let U denote the set of all cars in a dealer's lot and A = {the set of cars on the lot that are equipped with automatic transmission}
B = {the set of cars on the lot that are equipped with air conditioning}
C = {the set of cars on the lot that are equipped with a sun roof}
Find an expression in terms of A,B and C for each of the following sets:
[4] (a) The set of cars with at least one of the given options.
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[4] (b) The set of cars with exactly one of the given options.
[4] (c) The set of cars with automatic transmission and sun. roof but no air conditioning.
- Let U = {1,2,3,4,5,6,7} , A = {1,2,3} , B = {2,3,4,} and and C = {3,4,5,6}. Find:
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[16] (a)
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(c) (Ana)'
To help plan the number of meals to be prepared in a college cafeteria, a survey of 600 students was conducted and the following data were obtained: 175 students ate breakfast, 190 students ate lunch 275 students ate dinner, 68 students ate breakfast and lunch, 112 students ate breakfast and dinner, 90 students ate lunch and dinner and finally 32 students ate only breakfast and lunch (that is, they did not eat dinner).
Fill in the Venn diagram with the appropriate numbers (solve the Venn diagram), where B is the set of students who eat break- fast, L is the set of students who eat lunch and D is the set of students who eat dinner.
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[2] (b) How many students ate at least two meals?
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[5]
There are 2:00 seniors in Jefferson High School, of which 130 are males. It is known that 80% of the males and 60% of the females have their driver's license. A student is selected at random from this sienior class.
(a) What is the probability that the student is a female? F is -fh€ eve/i f 5-fwcteaf fc ex female. n - 5 /«» 4<a
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(b) What is the probability that the student is a male who has a driver's license.
[5]
O r*> +he ei/eof shsdent J^as <x * ill? x , drtver's license. aoo it_D— (c) Given that the student is a female, what is the probability that s;he has a driver's license.
[15] 9. The following table gives the grade distribution in a finite math class populated by freshman and sophomores only:
Freshmen
Sophomores Total
A
14 26
B 18 16 34
C 28 25 53
D 13 20 33
F 12 13 25
Total 83 88 171
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If a person is randomly selected from this class, what is the probability that the person:
(a) Is a freshman?
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(b) Received a B?
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(c) Is a sophomore or received an F?
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a 3^ (d)^ Is^ a^ freshman and^ received^ an A?
(e) Is a sophomore, given that the student received a D? a:110x3a.s97 fV,
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