Unions.

(a) Assume that $P(A)=0.4, P(B)=0.3$, and $P(C)=0.1$. If the events $A, B$, and $C$ are disjoint, find the probability that the union of these events occurs.

(b) Draw a Venn diagram to illustrate your answer to part (a).

(c) Find the probability of the complement of the union of $A, B$, and $C$.

Explain the difference between the intersection and the union of two sample spaces.

How has the government impacted the growth and stability of labour unions? Is your state a “right-to-work” state? Are there many union workers in your town or state? Do you see labour unions gaining strength or declining in your state in the future?

Which feature of a customs union differentiates it from a free trade area?

Why was capturing Vicksburg important to the Union?

Why did the Union ultimately prevail in the Civil War?

Your company is interesting in exploring international expansion into Africa. Visit the African Union’s website at https://au.int/en/. What are some of the countries included in the African Union? How easy will it be to approach entering these markets?

Visit the AFL-CIO website (www.aflcio.org) and find information about why workers join unions and what the benefits have been.$\newline$ Explain how union membership has affected minorities, women, older workers, and part-time workers.

Classify the variables. Use the EDSPEND data set for this exercise. Classify each variable as categorical or quantitative. Is there a label variable in the data set? If there is, identify it.

Express the following set using set-builder notation.

{Europe, Asia, Africa, North America, South America, Australia, Antarctica}

The population of ages at inauguration of all U.S. Presidents who had professions in the military is​ $62$, $46$,​ $68$, $64$, $57$. Why does it not make sense to construct a histogram for this data​ set?

$A)$ With a data set that is so small, the true nature of the distribution cannot be seen with a histogram.

$B)$ There must be an even number of data values in the data set to create a hstogram.

$C)$ Alecuate class boundaries for a histogram cannot be found with this data set.

$D)$ This data set would yield a histogram that is not bell-shaped.

In the following exercise state the cardinality of the given set.

The set of even integers greater than 20 and less than or equal to 40

Determine whether the following is a function.

Domain: A set of iPods

Correspondence: The number of Avril Lavigne songs on each iPod

Range: A set of numbers

In the following exercise use the roster method to identify the elements in the given set.

The solution set of $(x+2)^2=x^2+4 x+4$