Why calculate probabilities

The graph above illustrates the area of interest in the normal distribution. In order to determine the probability represented by the shaded area of the graph, use the standard normal Z-table provided at the bottom of the page.

Note that there are different types of standard normal Z-tables. The table below provides the probability that a statistic is between 0 and Z, where 0 is the mean in the standard normal distribution. There are also Z-tables that provide the probabilities left or right of Z, both of which can be used to calculate the desired probability by subtracting the relevant values. For this example, to determine the probability of a value between 0 and 2, find 2 in the first column of the table, since this table by definition provides probabilities between the mean which is 0 in the standard normal distribution and the number of choices, in this case, 2.

Note that since the value in question is 2. If, instead, the value in question were 2. Also, note that even though the actual value of interest is -2 on the graph, the table only provides positive values.

Since the normal distribution is symmetrical, only the displacement is important, and a displacement of 0 to -2 or 0 to 2 is the same, and will have the same area under the curve.

Thus, the probability of a value falling between 0 and 2 is 0. Since the desired area is between -2 and 1, the probabilities are added to yield 0. Returning to the example, this means that there is an The calculator also provides a table of confidence intervals for various confidence levels.

You first determine the event you are looking for, which is rolling a three on the first try, and then you divide this number by the number of total outcomes you can get. Since the die has six faces, you can assume that you can have six total possible outcomes.

Determining the likelihood of this event actually occurring is referred to as "the odds. Probability represents the likelihood of an event occurring for a fraction of the number of times you test the outcome. The odds take the probability of an event occurring and divide it by the probability of the event not occurring.

While the two mathematical concepts can be used together to solve various problems, you will need to calculate probability before determining the odds of an event taking place. Calculating probability with multiple random events is similar to calculating probability with a single event, however, there are several additional steps to reach a final solution.

The following steps outline how to calculate the probability of multiple events:. The first step for calculating the probability of multiple events occurring at the same time is to determine each of the events you want to work with. For instance, you might calculate the probabilities of rolling a six on two separate dice. Rolling each die separately represents one event. Using this example, we will calculate the probabilities of these two events occurring at the same time. Next, you can calculate the probability of rolling a six on one die and the probability of rolling a six on the other die.

Using these results, you can then find the total probability of these two events happening simultaneously. Finally, you can multiply each probability together to get a total probability for all events that can occur.

If you put money in a bank that is insured by the federal government and you don't exceed the maximum insured amount, the probability of losing your money is 0. But banks usually do not pay very much interest back to you on your savings. You have low risk and low rate of return. You've seen lots of ads on TV for trading stocks which means buying and selling stock in companies. Before buying a stock you need to investigate about the company. If the company makes a lot of money with their product and if you own some of their stock you may make more money too, potentially more money than what you could earn at the bank.

But if the company loses money, you may lose too. People who work with company finances calculate the probability that a company should make money and are a good company to invest money in. The following theorems of probability are helpful to understand the applications of probability and also perform the numerous calculations involving probability.

Theorem 1: The sum of the probability of happening of an event and not happening of an event is equal to 1. Theorem 2: The probability of an impossible event or the probability of an event not happening is always equal to 0.

Theorem 4: The probability of happening of any event always lies between 0 and 1. Theorem 5: If there are two events A and B, we can apply the formula of the union of two sets and we can derive the formula for the probability of happening of event A or event B as follows. Bayes' theorem describes the probability of an event based on the condition of occurrence of other events. It is also called conditional probability. It helps in calculating the probability of happening of one event based on the condition of happening of another event.

For example, let us assume that there are three bags with each bag containing some blue, green, and yellow balls. What is the probability of picking a yellow ball from the third bag? Since there are blue and green colored balls also, we can arrive at the probability based on these conditions also.

Such a probability is called conditional probability. If there are n number of events in an experiment, then the sum of the probabilities of those n events is always equal to 1. Let us check the below points, which help us summarize the key learnings for this topic of probability. Example 1: What is the probability of getting a sum of 10 when two dice are thrown?

Example 2: In a bag, there are 6 blue balls and 8 yellow balls. One ball is selected randomly from the bag. Find the probability of getting a blue ball. Example 3: There are 5 cards numbered: 2, 3, 4, 5, 6. Find the probability of picking a prime number, and putting it back, you pick a composite number. Example 4: Find the probability of getting a face card from a standard deck of cards using the probability formula. Probability is a branch of math which deals with finding out the likelihood of the occurrence of an event.

Probability measures the chance of an event happening and is equal to the number of favorable events divided by the total number of events. The value of probability ranges between 0 and 1, where 0 denotes uncertainty and 1 denotes certainty. The probability of any event depends upon the number of favorable outcomes and the total outcomes. In general, the probability is the ratio of the number of favorable outcomes to the total outcomes in that sample space.

The probability can be determined by first knowing the sample space of outcomes of an experiment. A probability is generally calculated for an event x within the sample space. The probability of an event happening is obtained by dividing the number of outcomes of an event by the total number of possible outcomes or sample space. The three types of probabilities are theoretical probability, experimental probability, and axiomatic probability.

The theoretical probability calculates the probability based on formulas and input values. The experimental probability gives a realistic value and is based on the experimental values for calculation.

Quite often the theoretical and experimental probability differ in their results. And the axiomatic probability is based on the axioms which govern the concepts of probability.

The conditional probability predicts the happening of one event based on the happening of another event. If there are two events A and B, conditional probability is a chance of occurrence of event B provided the event A has already occurred. The experimental probability is based on the results and the values obtained from the probability experiments. Experimental probability is defined as the ratio of the total number of times an event has occurred to the total number of trials conducted.

The results of the experimental probability are based on real-life instances and may differ in values from theoretical probability. The two important probability distributions are binomial distribution and Poisson distribution.

The binomial distribution is defined for events with two probability outcomes and for events with a multiple number of times of such events.

The Poisson distribution is based on the numerous probability outcomes in a limited space of time, distance, sample space. An example of the binomial distribution is the tossing of a coin with two outcomes, and for conducting such a tossing experiment with n number of coins.