statistics

A supplier shipped a lot of six parts (D1, D2, D3, A4, A5, A6) to a company. The lot contained three defective parts. Suppose the customer decided to randomly select two parts and test them for defects.

a. How large a sample space is the customer potentially working with?
b. List the sample space.
c. Using the sample space list, determine the probability that the customer will select a sample all acceptable part.
(Note: D = Defective part, A = Acceptable part)

a. There are

members of the sample space

b.

D1 D2, D1 D3, D1 A4, D1 A5, D1 A6D1 D2, D2 D3, D3 A5, D1 D3, D2 A4, D3 A6, D1 A4, D2 A5, A4 A5, D1 A5, D2 A6, A4 A6, D1 A6, D3 A4, A5 A6D1 D2, D2 D3, D1 D3, A4 A5, A5 A6, A4 A6D1 A4, D2 A5, D3 A6

c.

(Round your answer to 2 decimal places.)

problem 2

Given A = {1, 3, 5, 7, 8, 9}, B = {2, 4, 7, 9}, and C = {1, 2, 3, 4, 7}, solve the following.

a. $A\cup C=$

{7, 9}{1, 2, 3, 4, 5, 7, 8, 9}{1, 3, 7}

b. $A\cap B=$

{2, 4, 7, 9}{7, 9}{1, 2, 3, 4, 5, 7, 8, 9}

c. $A\cap C=$

{1, 2, 3, 4, 5, 7, 8, 9}{1, 3, 7}{1, 2, 3}

d. $A\cup B\cup C=$

{1, 3, 5, 7, 8, 9}{7}{1, 2, 3, 4, 5, 7, 8, 9}

e. $A\cap B\cap C=$

{1, 2, 3, 4, 7}{1, 2, 3, 4, 5, 7, 8, 9}{7}

f. $(A\cup B)\cap C=$

{1, 2, 3, 4, 7}{2, 4, 7}{1, 3, 7}

g. $(B\cap C)\cup (A\cap B)=$

{1, 3, 7}{1, 2, 3, 4, 5, 7, 8, 9}{2, 4, 7, 9}

h. A or B =

{1, 2, 3, 4, 5, 7, 8, 9}{7}{2, 4, 7, 9}

i. B and C =

{2, 4, 7}{1, 2, 3, 4, 5, 7, 8, 9}{7, 9}

problem 3

If a population consists of the positive even numbers through 30 and if A = {10, 6, 12, 28}, what is A’?

{2, 4, 8, 14, 16, 18, 20, 22, 24, 26, 30}{1, 3, 5, 7, 9, 11, 13, 15, 17, 19, 21, 23, 25, 27, 29}{0, 2, 4, 8, 14, 16, 18, 20, 22, 24, 26, 30}{1, 3, 5, 7, 9, 11, 13, 15, 17, 19, 21, 23, 25, 27, 29, 2, 4, 8, 14, 16, 18, 20, 22, 24, 26, 30}

problem 4

A company’s customer service 800 telephone system is set up so that the caller has six options. Each of these six options leads to a menu with four options. For each of these four options, three more options are available. For each of these three options, another three options are presented. If a person calls the 800 number for assistance, how many total options are possible?

problem 5

A bin contains six parts. Two of the parts are defective and four are acceptable.

a. If three of the six parts are selected from the bin, how large is the sample space?
b. Which counting rule did you use, and why?
c. For this sample space, what is the probability that exactly one of the three sampled parts is acceptable?

a.

b.

CombinationsPermutations

are used to counting the sample space because sampling is done

withoutwith

replacement.

c.

(Round your answer to 2 decimal places.)

problem 7

A small company has 10 employees. Four of these employees will be selected randomly to be interviewed as part of an employee satisfaction program. How many different groups of four can be selected?

problem 8

Given P(A) = .10, P(B) = .12, P(C) = .21, P(A$\cap$C) = .05, and P(B$\cap$C) = .03, solve the following. (Round your answers to 2 decimal places.)

a. P(A$\cup$C) =

b. P(B$\cup$C) =

c. If A and B are mutually exclusive, P(A$\cup$B) =