Question

Row 26 of the Excel file Census Education Data gives the number of employed persons in the civilian labor force having a specific educational level. a. Find the probability that an employed person has attained each of the educational levels listed in the data.b. Suppose that A is the event "An employed per-son has some type of college degree" and B is the event "An employed person has at least some col-lege." Find the probabilities of these events. Are they mutually exclusive? Why or why not?c. Find the probability P(A or B). Explain what this means.

Answer 1

Answer:

Step-by-step explanation:

Hello!

a. Find the probability that an employed person has attained each of the educational levels listed in the data.

You have 6 categories with the different levels of education of the employes.

1) Not a High school grad

2) High School graduate

3) Some college no degree

4) Associate's degree

5) Bachelor's degree

6) Advanced degree

To calculate the probabilities for each category you have to divide the observations of each category by the total of employes.

Total of employes: 11668755+36228706+20448104+9890659+22115069+10890838= 111242131

P₁= 11668755/111242131= 0.1048 ≅ 0.105

P₂= 36228706/111242131= 0.3256 ≅ 0.326

P₃= 20448104/111242131= 0.1838 ≅ 0.184

P₄= 9890659/111242131= 0.0889 ≅ 0.089

P₅= 22115069/111242131= 0.1988 ≅ 0.199

P₆= 10890838/111242131= 0.0978 ≅ 0.098

b. Suppose that A is the event "An employed person has some type of college degree" and B is the event "An employed person has at least some college." Find the probabilities of these events. Are they mutually exclusive? Why or why not?

A: "An employed person has some type of college degree"

B: "An employed person has at least some college."

Reminder two events are mutually exclusive when the occurrence of one of them keeps the other from occurring in a single repetition of the experiment. This means that they cannot occur at the same time or that the intersection between them is void and its probability cero.

Event A includes all the categories that refer to college degrees, that is 4) Associate's degree, 5) Bachelor's degree and 6) Advanced degree.

The event B includes "at least some college" this means a level of education starting from "incomplete college" to the highest degree, 3) Some college no degree, 4) Associate's degree, 5) Bachelor's degree, 6) Advanced degree.

As you can see, both events have categories in common which means that they are not mutually exclusive and they can happen at the same time.

P(A)= P₄ + P₅ + P₆ = 0.089 + 0.199 + 0.098= 0.386

P(B)= P₃ + P₄ + P₅ + P₆ = 0.184 + 0.089 + 0.199 + 0.098= 0.57

c. Find the probability P(A or B). Explain what this means.

This probability is the union between the two events and you can calculate it following the theorem:

P(A∪B)= P(A) + P(B) - P(A∩B)

Since both events aren't mutually exclusive, when you add both probabilities, the elements they have in common are counted two times, that is why you need to subtract the probability of their intersection.

P(A∩B)= P₄ + P₅ + P₆ = 0.386

P(A∪B)= 0.386 + 0.57 - 0.386= 0.57

I hope it helps!