Sample Problems For Exam 3 in Applied Finite Mathematics | Exams Mathematics

Sample Problems For Exam 3

Spring 2005 Compiled by Joe Kahlig

This collection of questions is intended to give you an idea of different types of question that might be asked on

the exam. There may be questions on the exam that are not found on this handout.

These questions cover chapter 7 and Sections 8.1-8.4 in the Applied Finite Mathematics, 6th edition by S. T. Tan.

Video solutions can be found at this link: http://www.math.tamu.edu/∼kahlig/exam.info/Finite-examinfo.html

1. An experiment consists of tossing a 4 sided die and flipping a coin.

(a) Describe an appropriate sample space for this experiment.

(b) Are the events, E: getting a head and F: rollind a 2 on the die, mutually exclusive? Justify your answer.

2. Explain the difference between mutually exclusive and independent.

3. Roll a 10 sided die and an 8 sided die. What is the probability that

(a) A sum of 3 or a sum of 6 is rolled?

(b) A sum of 6 or one of the die(at least one die) has a 2 on it.

(d) A sum of 12 is rolled provided a six is cast (at least one six is rolled).

(e) A sum of 8 and a 6 is rolled on one of the die.

4. Is the statement correct or incorrect? Explain your answer. The probability that as certain stock will

increase in value over a period of one week is .6. Therefore, the probability that the stock will decrease in

value is .4.

5. Jim has a drawer containing eight blue, five black, and six white socks. If he pulls out two socks at random,

what is the probability that Jim will draw a matching pair of socks?

6. A box contains four red, five white, and eight yellow marbles. Two marbles are drawn without replacement.

(a) What is the probability that the first marble is red?

(b) Assuming that the first marble is red, what is the probability that the second marble drawn is red?

7. A student takes a 10 question multiple choice exam in which each question has 4 answers. Being unprepared

for the exam, the student randomly guesses at each of the question.

(a) What is the probability of getting exactly 6 of the questions correct?

(b) What is the probability of passing the exam? (Grades below 70 don’t pass.)

(d) How many questions should the student expect to get correct?

8. The weather forecaster at station WIBV is correct 82% of the time; the forecaster at neighboring station

WILA, 65% of the time. If the forecasters make their weather predictions independently of each other, what

is the probability that on a given occasion, one of the two (or both) will be correct?

9. A manufacturer of automobiles receives 500 car radios from each of three different suppliers. Unknown to

the manufacturer, there are five defective radios from supplier A, seven from supplier B, and only two from

supplier C. As a means of quality control, one radio is selected at random from each of the shipments. What

is the probability that

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Download Sample Problems For Exam 3 in Applied Finite Mathematics and more Exams Mathematics in PDF only on Docsity!

Sample Problems For Exam 3

Spring 2005 Compiled by Joe Kahlig

This collection of questions is intended to give you an idea of different types of question that might be asked on the exam. There may be questions on the exam that are not found on this handout. These questions cover chapter 7 and Sections 8.1-8.4 in the Applied Finite Mathematics, 6th^ edition by S. T. Tan.

Video solutions can be found at this link: http://www.math.tamu.edu/∼kahlig/exam.info/Finite-examinfo.html

An experiment consists of tossing a 4 sided die and flipping a coin. (a) Describe an appropriate sample space for this experiment. (b) Are the events, E: getting a head and F: rollind a 2 on the die, mutually exclusive? Justify your answer.
Explain the difference between mutually exclusive and independent.
Roll a 10 sided die and an 8 sided die. What is the probability that (a) A sum of 3 or a sum of 6 is rolled? (b) A sum of 6 or one of the die(at least one die) has a 2 on it. (c) A sum of 8 is rolled if the ten sided die has an even number on it. (d) A sum of 12 is rolled provided a six is cast (at least one six is rolled). (e) A sum of 8 and a 6 is rolled on one of the die.
Is the statement correct or incorrect? Explain your answer. The probability that as certain stock will increase in value over a period of one week is .6. Therefore, the probability that the stock will decrease in value is .4.
Jim has a drawer containing eight blue, five black, and six white socks. If he pulls out two socks at random, what is the probability that Jim will draw a matching pair of socks?
A box contains four red, five white, and eight yellow marbles. Two marbles are drawn without replacement. (a) What is the probability that the first marble is red? (b) Assuming that the first marble is red, what is the probability that the second marble drawn is red? (c) What is the probability that a red marble is not drawn in neither the first nor second draw?
A student takes a 10 question multiple choice exam in which each question has 4 answers. Being unprepared for the exam, the student randomly guesses at each of the question. (a) What is the probability of getting exactly 6 of the questions correct? (b) What is the probability of passing the exam? (Grades below 70 don’t pass.) (c) What is the probability that the student get the first three correct and the last 7 wrong? (d) How many questions should the student expect to get correct?
The weather forecaster at station WIBV is correct 82% of the time; the forecaster at neighboring station WILA, 65% of the time. If the forecasters make their weather predictions independently of each other, what is the probability that on a given occasion, one of the two (or both) will be correct?
A manufacturer of automobiles receives 500 car radios from each of three different suppliers. Unknown to the manufacturer, there are five defective radios from supplier A, seven from supplier B, and only two from supplier C. As a means of quality control, one radio is selected at random from each of the shipments. What is the probability that

(a) All the radios selected are in working order? (b) At least one of the selected radios is defective? (c) exactly one of the selected radios is defective?

A new test for Alzheimer’s Disease will detect the disease 95% of the time in a person who has Alzheimer’s and will fail to detect it 5% of the time. In addition, the test will give a false positive 15% of the time. If the test is give to a person selected at random from a group of subjects, 90 of whom are healthy and 10 of whom have Alzheimer’s, what is the probability that (a) Alzheimer’s will not be detected if the person has the disease? (b) the person has Alzheimer’s if the test detects the disease? (c) If the person takes the test twice, what is the probability that the person has the disease if both test are positive.
A chef’s school is 60% male. Seventy percent of the males and 90% of the females like eating crab legs for dinner. A student of the school is selected at random. (a) What is the probability that the student is male or likes eating crab legs for dinner? (b) If the student likes eating crab legs for dinner, what is the probability that the student is female? (c) What percentage of the students like eating crab legs for dinner?
Let E and F be two events and P (E) = .35, P (F ) = .55, and P (E ∩ F C^ ) = .15. Answer the following questions.

(a) P (E ∩ F ) = (b) Compute the probability of exactly one of these events occurring. (c) Are E and F mutually exclusive? (d) Are E and F independent? (e) P (E|F ) = (f) P (E ∪ F ) =

Classify the following random variables as finite discrete, infinite discrete, or continuous.

(a) X = The number of times a die is cast until a 5 is rolled. (b) X = How long it takes you use an ATM machine. (c) X = The number of cadets in a class of 100 students. (d) X = The temperature of the human body.

Fifteen people are selected at random. What is the probability that at least 2 of the people in this group

(a) were born on the same day? (b) were born in the same month? Assume that months are equally likely.

The accompanying data were obtained in a study conducted by the manage of the Sav-More Supermarket. In this study the number of customers waiting in line at the express checkout at the beginning of each 3-minute interval between 9 a.m. and 12 noon on Saturday was observed. Number of Customers 0 1 2 3 4 5 6 7 8 9 10

Frequency 1 4 2 7 14 8 10 6 3 4 1

Sample Problems For Exam 3 in Applied Finite Mathematics, Exams of Mathematics

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