Probability is used in many ways. It can be formalized as a mathematical formula or as a set of axioms by which it can be deduced from other information. The more formal approach to probability uses complex mathematics, while the axiomatic approach relies on experience. Although they are not completely different, they use slightly different concepts. There is no significant difference between them, but the way they are formulated has some differences.
To begin with, it should be noted that most of us will never directly come into contact with probability. Most of the time it will occur when we observe or attempt to predict an outcome of an experiment. We may expect the ball to fall on the floor if the fair is fair, or we may expect the cat to jump off the table if the cats are mice.
Probability is an important concept in statistics, probability theory, statistics, and in the scientific method itself. To get a graphical representation of probability, we need to introduce the concept of random variables. These variables can be thought of as being “free.” The probability of their presence (i.e., their probability of being “uncharacteristically distributed”) is always equal to their mean value. For example, two given values of x and y are both uniformly distributed over the range [0,1], so their probability values are both 1.
Probability can also be viewed in terms of tails and heads, where heads are the complete sets of probability outcomes for any sample or experiment. Heads can either be “in the lead” or “lagging behind.” A “head” in this situation represents a possibility only because the sample or experiment goes in one direction or the other. In this sense, probability can be seen as a state of a change from a total state of zero (no probability) to a total state of one (a probability outcome). In this way, the probability can be thought of as a function of the total number of possibilities.
A probability tree diagram can help you visualize probability better. A probability tree diagram starts with a start value, called the x value, and branches off into smaller branches as the probability of each branch increases. For example, the first probability level is the easiest to reach, since you would only need to look at the starting total number of possible outcomes, and determine whether or not you’re leaning toward a head or a tail. Each subsequent level of probability adds a little more work, as the branches become narrower and thinner.
When it comes to calculating theoretical probability, you’ll use one of two standard methods. The first method, called the logistic regression, involves finding the probability of one variable given its corresponding figure for another variable. Using the log-normal distribution, you can calculate the probability of the data you’ve already collected, on the average over the range of values you want to estimate. This makes it much easier to determine the value of each variable and allows you to combine results from multiple variables.
The other method for calculating theoretical probability, which we’ll use for our real life experiments, is called the binomial expectation. Using binomial expectation, you take the normal distributions and randomize them, assigning probabilities to the outcomes. You then take the binomial distribution over the set of outcomes and calculate the expected frequency of occurrence, given the probability of those outcomes. With both methods, you take a sample of some sort, and look for a distribution that coincides with the sample. Once you find such a distribution, you can then use it to calculate the probability of the outcome and see whether your experimental outcomes are consistent with the theoretical probability you calculated.