Question

Using the table containing the breakdown of all employees on nonfarm payrolls in the United States during March 2014, findthe probability that a randomly selected U.S. worker was not in either Wholesale Trade or Education & Health Services.Express your answer as a fraction in lowest terms or a decimal rounded to the nearest millionth.

Answer 1

The probability that a randomly selected U.S. worker was not in either Wholesale Trade or Education & Health Services is 0.801055

Finding the probability of not being in Wholesale Trade or Education & Health Services

From the question, we have the following parameters that can be used in our computation:

The table of values

Where, we have

Wholesale Trade = 5,803.7

Education & Health Services = 21,481.0

Total = 137,147.0

So, the required probability is

P = 1 - P(Wholesale Trade) - P(Education & Health Services)

This gives

P = 1 - (5,803.7/137,147.0) - (21,481.0/137,147.0)

Evaluate

P = 0.801055

Hence, the probability is 0.801055

Answer 2

Using the data of the table, we must find the probability that a randomly selected U.S. worker was not in either Wholesale Trade or Education & Health Services.

Let's define the following events:

• A = an employee works at Wholesale Trade,

,

• B = an employee works at Education & Health Services.

Now, the probability that an employee works in a particular area, it is equal to the quotient between the number of employees in that area and the total number of employees.

Using the data of the table we find that:

• P(A) = # employees at Wholesale Trade / total # of employees = 5,803.7/137,147.0 ≅ 0.04231226.

,

• P(B) = # employees at Education & Health Services / total # of employees = 21,481.0/137,147.0 ≅ 0.15662756.

Now, the probability that an employee is not in either Wholesale Trade or Education & Health Services, is given by:

`P=1-P(A)-P(B)=1-(5,803.7)/(137,147.0)-(21,481.0)/(137,147.0)=(137,147.0-5,803.7-21,481.0)/(137,147.0)=(109,862.3)/(137,147.0),`

or to the nearest millonth:

`P=1-P(A)-P(B)\cong1-0.04231226-0.15662756\cong0.80105507\cong0.801055.`

Answer

The probability that a randomly selected U.S. worker was not in either Wholesale Trade or Education & Health Services is:

`P=(109,862.3)/(137,147.0),`

or to the nearest millonth:

`P\cong0.801055.`