The U.S. Census Bureau serves as the leading source of quantitative data about the nation’s people and economy. The following cross-tabulation shows the number of households (1,000s) and the household income by the highest of level of education for the head of the household (U.S. Census Bureau website, 2013). Only households in which the head has a high school diploma or more are included. What is the probability of one of these households having an income below $25,000? What is the probability of a household headed by someone with a bachelor’s degree earning less than $25,000? Is household income independent of educational level? Highest Level of Education Household Income Under $25,000 $25,000 to $49,999 $50,000 to $99,999 $100,000 and Over TOTAL High School Graduate 9880 9970 9441 3482 32,773 Bachelor’s Degree 2484 4164 7666 7817 22,131 Master’s Degree 685 1205 3019 4094 9003 Doctoral Degree 79 160 422 1076 1737 TOTAL 13,128 15,499 20,548 16,469 65,644
Compound Probability
Compound probability can be defined as the probability of the two events which are independent. It can be defined as the multiplication of the probability of two events that are not dependent.
Tree diagram
Probability theory is a branch of mathematics that deals with the subject of probability. Although there are many different concepts of probability, probability theory expresses the definition mathematically through a series of axioms. Usually, these axioms express probability in terms of a probability space, which assigns a measure with values ranging from 0 to 1 to a set of outcomes known as the sample space. An event is a subset of these outcomes that is described.
Conditional Probability
By definition, the term probability is expressed as a part of mathematics where the chance of an event that may either occur or not is evaluated and expressed in numerical terms. The range of the value within which probability can be expressed is between 0 and 1. The higher the chance of an event occurring, the closer is its value to be 1. If the probability of an event is 1, it means that the event will happen under all considered circumstances. Similarly, if the probability is exactly 0, then no matter the situation, the event will never occur.
- The U.S. Census Bureau serves as the leading source of quantitative data about the nation’s people and economy. The following cross-tabulation shows the number of households (1,000s) and the household income by the highest of level of education for the head of the household (U.S. Census Bureau website, 2013). Only households in which the head has a high school diploma or more are included.
- What is the
probability of one of these households having an income below $25,000? - What is the probability of a household headed by someone with a bachelor’s degree earning less than $25,000?
- Is household income independent of educational level?
- What is the
|
Highest Level of Education |
Household Income |
||||
|
Under $25,000 |
$25,000 to $49,999 |
$50,000 to $99,999 |
$100,000 and Over |
TOTAL |
|
|
High School Graduate |
9880 |
9970 |
9441 |
3482 |
32,773 |
|
Bachelor’s Degree |
2484 |
4164 |
7666 |
7817 |
22,131 |
|
Master’s Degree |
685 |
1205 |
3019 |
4094 |
9003 |
|
Doctoral Degree |
79 |
160 |
422 |
1076 |
1737 |
|
TOTAL |
13,128 |
15,499 |
20,548 |
16,469 |
65,644 |
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