Question

Do the following problems. 1. Each of three barrels from a manufacturing line are classified as either above (a) or below (b) the target weight. Provide the ordered sample space. 2. The heat on each of two soldered parts is measured and labeled as either low (l), medium (m), or high (h). State the number of elements in the ordered sample space. 3. Consider the set of Beatles songs with a primary writer as either Paul McCartney (P) or John Lennon (J). From this set, ten songs were randomly chosen and classified by their main composer (i.e. primary writer). State the number of elements in the ordered sample space. NOTE: both artists composed many songs, way more than 10. 4. The following two questions appear on an employee survey questionnaire. Each answer is chosen from the five-point scale of 1 (never), 2, 3, 4, 5 (very often). i.) How often do you interact with the marketing team? ii.) How often do you interact with the accounting team? State the ordered sample space. HINT: Consider each person’s response to be a two-digit number. You MUST state the total number of elements in this sample space for full credit. 5. The concentration of chlorine in the air is measured in parts per billion (PPB) and recorded to the nearest PPB. State the sample space. 6. This experiment involves repeatedly calling a busy phone line until a connection is made. Provide the sample space. 7. Use a Venn diagram to verify that (A ∩ B) 0 = A0 ∪ B0 8. Suppose you want to make a sandwich and you can choose either white, rye, or wheat bread, and you can choose either ham or turkey and you can choose either cheese or no-choose. Describe the set of all possible sandwiches using a tree diagram. 9. A set of 8 operations can be done in any order. How many unique orderings are there? {more on next page...} 1 10. A manufacturing process consists of 8 operations, however, the 3 machining operations must be completed before the remaining 5 assembly operations can begin. The 3 machining operations can be done in any order, as can the 5 assembly operations. How many different production sequences are possible? 11. Three attempts are made to read data in a magnetic storage device before an error recovery procedure is used. If there are three failures, then there is a subsequent error recovery procedure that attempts up to two repositionings before an “abort” message is sent. Let s denote the success of a read operation f denote the failure of a read operation S denote the success of an error recovery procedure F denote the failure of an error recovery procedure A denote an abort message sent. State the sample space of this experiment. 12. Samples of emissions for three suppliers are classified for conformance to air-quality specifications. The results from 100 samples is summarized as follows: Conforms Yes No 1 20 8 Supplier 2 27 10 3 30 5 Let A be the event that a sample is from supplier 1 and B be the event that a sample conforms to specifications. Determine the number of samples in A0 ∩ B, B0 , A ∪ B. 13. In a sheet metal operation, 5 notches and 4 bends are required. The notches are indistinguishable from each other, as are the bends. If the operations can be done in any order, how many distinct ways of completing the manufacturing are possible? 14. In a chemical plant, 24 holding tanks are used for final product storage. Four tanks are selected at random without replacement. Suppose that six of the tanks contain material in which the viscosity exceeds the customer requirements. What is the probability that exactly one tank in the sample contains high-viscosity material? 15. Consider picking a number at random from the set of counting numbers from 1 to 25. (a) Describe the sample space S. (b) Let T denote the event that the number drawn is divisible by 3. Describe T. (c) Let B denote the event that the number drawn is a prime number. Describe B. (d) Describe the event B0 (e) Describe the event T ∩ B {more on next page...} 2 16. Consider an experiment where two 6-sided dice are rolled. We can describe the ordered sample space as below where the first coordinate of the ordered pair represents the first die and the second coordinate represents the second die. (a) Describe the event E that the sum of the two dice is 5. (b) Describe the event F that the number of the first die is exactly 1 more than the number on the second die. (c) If the dice are ‘fair’, are all 36 of these possible outcomes equally likely? 17. Your garage door has an outdoor key-pad (with the numbers 0 to 9 on it) that uses a 4-digit code. Suppose a thief approaches your garage and notices that four particular numbers are very well-used. If we assume the code uses all four numbers exactly once, what is the maximum number of 4-digit codes the thief has to try? 18. Suppose a coin is tossed, then a 6-sided die is rolled, then a card is chosen from a 52- card deck. Use the multiplication rule for counting to determine how many elements are in the sample space.

Answer #1

Question 1: Roll two fair dice. Then the sample space S is the
following.
S =
(1,1) (1,2) (1,3) (1,4) (1,5) (1,6)
(2,1) (2,2) (2,3) (2,4) (2,5) (2,6)
(3,1) (3,2) (3,3) (3,4) (3,5) (3,6)
(4,1) (4,2) (4,3) (4,4) (4,5) (4,6)
(5,1) (5,2) (5,3) (5,4) (5,5) (5,6)
(6,1) (6,2) (6,3) (6,4) (6,5) (6,6)
Let E be the event that the sum of the dice is odd, let F be the
event that the first die lands on 1,
and let G...

1) In a college, each student ID card is linked with a unique
5-digit pin from the set {0,1,2,3,4,5,6,7,8,9}. A) Find the number
of ID cards possible. B) Find the number of ID cards possible if
the 5-digit number is an odd number? C) Recalculate A&B if the
digits are not allowed to be repeated.
2) A license plate has 3 letters followed by 4 digits. How many
different license plate numbers can be formed if the letters cannot
be...

1. Indicate if each of the following is true or false. If false,
provide a counterexample.
(a) The mean of a sample is always the same as the median of
it.
(b) The mean of a population is the same as that of a
sample.
(c) If a value appears more than half in a sample, then the mode
is equal to the value.
2. (Union and intersection of sets) Let Ω = {1,2,...,6}. Suppose
each element is equally likely,...

Do all the following problems.
I. Choose the best answer for each
multiple choice. Please use CAPITAL letters to indicate your answer
and write neatly. (30 points)
1. ____ 4.____ 7. ____ 10.____ 13.
____
2. ____ 5.____ 8. ____ 11.____ 14.
____
3. ____ 6.____ 9. ____ 12.____ 15.
____
Whenever the population standard deviation is unknown and the
population has a normal or near-normal distribution, which
distribution is used in developing an interval estimation?
A. standard distribution
B....

1.To win the Michigan Lotto a person must correctly pick 6
distinct numbers from the numbers 1 through 46. A lotto ticket cost
$1. If you buy 1000 tickets (and choose different sets of six
numbers for each tickets, of course), What is the probability that
you will have the winning set numbers?
2.Salespersons Adams and Jones call on three and four customers,
respectively, on a given day. Adams could make 0, 1, 2, or 3 sales,
whereas Jones could...

1. A random number generator is used to select a number from 1
to
500 ?(inclusively).
What is the probability of selecting the number 595
?
What is the probability?
2.Identify the sample space of the probability experiment and
determine the number of outcomes in the sample space.
-Randomly choosing an even number between 10 and 20,
inclusive
The sample space is?
(Use a comma to separate answers)
There are _____ outcomes in the sample space
3. Determine the number...

1) At a lumber company, shelves are sold inȱȱ5 types of wood, 4
different widths and 3 different lengths. How many different types
of shelves could be ordered?
2) A shirt company has 5 designs each of which can be made with
short or long sleeves. There are 4 different colors available. How
many differentȱȱshirts are available from this company? Find the
indicated probability. Round your answer to 2 decimal places when
necessary.
3) A bag contains 6 red marbles,...

1) Describe an example of each of the following that may be
found of your kitchen: Explain how your choice falls into this
category, and if there is a chemical name or symbol for it, provide
that as well. Provide a photo of your example with your ID card in
it. a) a compound b) a heterogeneous mixture c) an element (symbol)
Moving to the Caves… Lechuguilla Caves specifically. Check out this
picture of crystals of gypsum left behind in...

1. Answer EITHER part (a) OR part (b). (a) A gas scrubber on an
oilrig discharged gas periodically such that an accumulation of
hydrocarbon gas nearby had occurred. A contractor welder was
dispatched to a job immediately adjacent to the area and it being a
shift change and personnel unavailable temporarily, the welder
decided to commence welding. As a consequence, an incident
occurred. Describe briefly: (i) what you imagine was the incident
including any hazards existing prior to or during...

MATHEMATICS
1. The measure of location which is the most likely to
be
influenced by extreme values in the data set is the a. range
b.
median c. mode d. mean
2. If two events are independent, then a. they must be
mutually
exclusive b. the sum of their probabilities must be equal to one
c.
their intersection must be zero d. None of these alternatives
is
correct. any value between 0 to 1
3. Two events, A and B,...

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