## 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 non-mutually 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 non-mutually exclusive events is denoted by:

P(Y u Z) = P(Y) + P(Z) - P(Y n Z)

Next Up

## 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.

RELATED TERMS
1. ### Mutually Exclusive

Mutually exclusive is a statistical term used to describe a situation ...
2. ### Joint Probability

A joint probability is a statistical measure where the likelihood ...
3. ### Posterior Probability

Posterior probability is the revised probability of an event ...
4. ### Bayes' Theorem

Bayes' theorem is a mathematical formula for determining conditional ...
5. ### Expected Value

Anticipated value for a given investment. In statistics and probability ...
6. ### Yearly Probability Of Dying

Yearly Probability Of Dying is a numerical figure that depicts ...
Related Articles
1. Investing

### What Happens To Your Student Debt If You Die?

What happens to student debt when you die? It all depends on the lending agency.
2. 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.
3. Personal Finance

### Financial Solutions For Young Women

Break through the stereotypes and find out how to manage your life to meet your needs.
4. 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.
5. Personal Finance

### Does It Make Sense to Go to College in Europe?

If you're deciding whether to get a degree abroad, first do your research and talk to alumni who have completed the same program.
6. 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.
7. 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.
8. 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 ...
9. Personal Finance

### 5 Worst Money Mistakes You Can Make In College

Watch out for these costly mistakes while in school.
10. Personal Finance

### Benefits Of Concurrent Enrollment

College tuition is rising. See what you can do for your child now to give them a head start.
Hot Definitions
1. ### Investment Advisor

An investment advisor is any person or group that makes investment recommendations or conducts securities analysis in return ...
2. ### Gross Margin

A company's total sales revenue minus its cost of goods sold, divided by the total sales revenue, expressed as a percentage. ...
3. ### Inflation

Inflation is the rate at which prices for goods and services is rising and the worth of currency is dropping.
4. ### Discount Rate

Discount rate is the interest rate charged to commercial banks and other depository institutions for loans received from ...
5. ### Economies of Scale

Economies of scale refer to reduced costs per unit that arise from increased total output of a product. For example, a larger ...
6. ### Quick Ratio

The quick ratio measures a company’s ability to meet its short-term obligations with its most liquid assets.
Trading Center