What is the 'Addition Rule For Probabilities'
The addition rule for probabilities describes two formulas, one for the probability for either of two mutually exclusive events happening and the other for the probability of two nonmutually events happening. The first formula is just the sum of the probabilities of the two events. The second formula is the sum of the probabilities of the two events minus the probability that both will occur.
Mathematically, the probability of two mutually exclusive events is denoted by:
P(Y u Z) = P(Y) + P(Z)
Mathematically, the probability of two nonmutually exclusive events is denoted by:
P(Y u Z) = P(Y) + P(Z)  P(Y n Z)
BREAKING DOWN 'Addition Rule For Probabilities'
To illustrate the first rule in the addition rule for probabilities, consider a die with six sides and the chances of rolling either a 3 or a 6. Since the chances of rolling a 3 are 1 in 6 and the chances of rolling a 6 are also 1 in 6, the chances of rolling either a 3 or a 6 are: 1/6 + 1/6 = 2/6 = 1/3.
To illustrate the second rule, consider a class in which there are 9 boys and 11 girls. At the end of the term, 5 girls and 4 boys receive a grade of B. If a student is selected by chance, what are the odds that the student will be either a girl or a B student? Since the chances of selecting a girl are 11 in 20, the chances of selecting a B student are 9 in 20 and the chances of selecting a girl who is a B student are 5/20, the chances of picking a girl or a B student are: 11/20 + 9/20  5/20 =15/20 = 3/4.
In reality, the two rules simplify to just one rule, the second one. That's because in the first case, the probability of two mutually exclusive events both happening is 0. In the example with the die, it's impossible to roll both a 3 and a 6 on one roll of a single die. So the two events are mutually exclusive.

A Priori Probability
A priori probability is a likelihood of occurrence that can be ... 
Event Study
An event study is an empirical analysis done on a security that ... 
Accounting Event
An accounting event is a transaction that is recognized in the ... 
Default Probability
Default probability is the likelihood over a specified period, ... 
Yearly Probability Of Living
Yearly probability of living is a numerical figure that depicts ... 
Expected Value
The expected value is the anticipated value for a given investment ...

Retirement
Student Loan Debt and Your Retirement Savings
The burden of student loan debt can hinder the ability to save long term for retirement 
Personal Finance
What New Student Loan Repayment Options Mean
American college graduates are facing an increasing amount of student loan debt. There are new rules for repaying that debt. Here's what you need to know. 
Tech
1 in 5 College Students Used Loans for Cryptocurrency Investments
Seven in 10 seniors set to graduate this spring have more than $37,000 in student loans. More than 20% used loans to invest in cryptocurrency. 
Personal Finance
10 Ways Student Debt Can Destroy Your Life
If you're getting a student loan, think critically about how you will manage your loan. Student debt could have a profound negative impact on your life. 
Personal Finance
Four Critical Financial Decisions Facing College Students
The financial decisions students make in college can affect academic achievement, wellbeing and postgraduate success. 
Personal Finance
Why Student Loan Debt Might Be the Next Financial Crisis
The increasing student loan debt may turn into the next financial crisis in the U.S. Here's why. 
Personal Finance
9 Student Discounts You Shouldn't Miss
College students can always stand to save some cash. Here are nine discount opportunities students should explore and exploit. 
Personal Finance
How Student Debt Imperils Retirement Savings
Student loan debt is out of control. Here is how it can impact saving for retirement. 
Trading
The Math Behind Betting Odds & Gambling
A betting odd opportunity should be considered valuable if the probability assessed for an outcome is higher than the implied probability estimated by the bookmaker. Read more on the math behind ... 
Personal Finance
American Debt: Student Loan Debt Up $21 Billion
It isn’t news that student loan debt is large and growing, up $21 billion in Q4. What would be news is a solution to the problem.

Can student loans be used to pay rent?
In most cases, loans can be used for housing costs, but students should still plan to have some cash on hand. Read Answer >>