# How to find Probability and Expected Value in Mathematics?

Mathematics is the major science that helps in understanding the basic concepts of numbers, counting, measurements, shapes of objects etc. It has some other branches that deal with different aspects of the calculations and possibilities. Here we can summarize the concepts of probability and expected value.

Probability is the quality of expected and it is the possible outcomes of any event before its occurrence. Another type of discussion is the expected value. It is a probability theory and defining as the expectation of the outcomes in response to any kind of inputs or actions that we put in. In this article the complete discussion about finding the probability and expected value in mathematics and their important features in search of the findings.

**What is probability?**

At the initial step the probability is defining as something that is likely to happen. This means it has the possible outcomes of the occurrence of any event. The outcome of any event without happening is not possible but it can be determined by one and only thing that is “chance”. For example, when rolling a ludo dice at its first attempt there would be the probability of ludo dice is 6. After every trial the probability of the desired number is determined by the chance of it rolling and sideways.

**How to find probability?**

Probability might be used in different situations, businesses and firms for their developing strategies, marketing plans, revenues, sales and expenditure ideas that used to run or drive a business. In case of multiple events the probability can be found by smashing down the probability into a separate calculation. Then the probability is multiplying consequences altogether to achieve the single possible outcome. Some of the steps that helps in finding or calculating the probability can be described as follows:

- Regulates a single event with single outcome
- Recognize the total number of outcomes
- Division of number of events by the number of possible outcomes.

These are the steps that we must have to follow for finding the probability, we can also find the probability online by using probability calculator with steps.

**Formula for probability**

The formula for probability refers to the possibility that events need to happen, and can explain as equal to the ratio of the numbers of the favorable outcomes and the total number of outcomes. The mathematical expressions for the formula of probability can write as follows:

**Probability P ( E ) = Number of favorable outcomes / Total number of outcomes**

In this formula the P ( E ) belongs to the probability of an event to happen. Through this formula the solution to any event, situation or probability can easily calculate.

**What is the expected value?**

Expected value can define as the probability that will multiply by the value of every outcome. As its name indicates, it is the estimation or average values that we can use in the case of random variables. It is the probability distribution that helps in conducting the average or mean of any kind of random variable. Expected value has different patterns to calculate the variables. Some of them particularly need the integrals to be used in the situation of continuous variables. Through this calculation we can find the centre of the variable or the average of the random variable.

**Categories of expected value**

Expected values have categories that calculated different amounts of variables that can be expressed as

- Single discrete variables
- Single continuous variables
- Multiple discrete variables
- Multiple continuous variables

**How to find expected value?**

In simple words the expected value can measure by multiplying every possible outcome by the given value that will occur. After that possible outcomes multiplication the all values will added up to conclude the average result of the expected value. The possibilities of every outcome related to every new chance that arises in the process of expected value.

For example, the use of expected value in a game of 3 bottles that has 3 chances of playing and winning the price. The first turn of rolling bottle has the chances of ⅓ to win the game, the second rolling has chances of ⅔ and third has the 3/3. The final outcome will calculate after the summation of all random values i.e. ⅓ + ⅔ + 3/3= 2

Hence prove that the chances of winning the bottle game would be 2 after the proper estimation of expected values.

Related: One may also check the answer of the problem online. As there are a lot of online expected outcome calculator available for calculating expected value with in a second with all possible steps in its calculation.

**Formula for expected value**

The mathematical representation of the general formula for expected value are as follows;

**EV ***= ∑ P ***( x ) * n )**

The description of expected value formula is as follows

EV = the expected value

∑ = the sigma notation

P = the probability

X = the event that will multiply

n = n is the amount of time that will happen after and after

The following formula for expected value is helpful in daily life for the estimation of investment, currency, travelling expenditures and also the chances of winning prize money or games.