Learning Probability in an Age of Technology

What is Probability in Statistics

The likelihood or prospect chances of an event to occur is known as probability. For instance, the chance of turning a coin and being tails is 1⁄2, as there is one method to get a tail and the total number of results is 2 i.e. either a head or a tail.

Probability = amount of ways to succeed / the total potential results

Thus, according to the given example the probability (P) can be represented as P (tails) = ½. We can say that, it is all about arranging experiments and comparing the number of possible outcomes to the number of possibilities you desire in order to determine probability.

Types of Probability 

Conditional Probability

The type of probability in which one event will occur if another event previously occurred is the conditional probability. Conditional probability formula is:

P (A|B) = P (A and B)/P(B)

Theoretical Probability

The probability that is predicated on the likelihood that something will occur in the future. The logic underlying probability serves as the foundation for the theoretical probability. In the case of a coin flip, for instance, the theoretical chance of obtaining a head is 1 out of 2 trials.

Experimental Probability

The defining statistics of the experimental probability contain the numbers of trials, in contrast to theoretical probability definition. Assume that a coin is flipped 20 times and we have tails out of these 20 times 7 times, then the experimental probability is 7/20.

This probability calculation is based on the trials already being conducted. The probability of experimentation is equal to the number of possible results for an event divided by the total number of trials.

Probability Rules

There are three key probability rules i.e. the multiplication rule addition rule and the complementary rule. The complementary rule however is also known as “the subtraction rule” sometimes as it contains subtraction operations.

These rules are used to calculate probability manually but nowadays there are a lot of online probability calculator tools which helps students as well as teachers for solving probability online.

The Rule of Additions:

If there are two events as A and B and both are mutually exclusive or are not able to take place concurrently, the third term shall be 0, and the rule shall be reduced to P(A or B) = P(A) + P(B).

You can’t, for instance, flip a coin and bring it on a toss with both heads and tails at the same time. This rule of probability, the addition rule is mathematically represented as;

P (A or B) = P(A) + P(B) – P (A and B)

Rule of Multiplication:

When A and B are separate occurrences i.e. as independent events, the formula may be concluded as P (A and B) = P(A)* P (B). The term “independent” means any event whose result is not influenced by the outcome of another event.

Take the second try of two flips of a coin as an example, which still has a half (50%) chance of coming up as heads, independent of what occurred in the first flip. How likely are you to find tails on the first flip of a coin and heads on its second flip during these two coin flips?

The formula for the multiplication rule is given below. Moreover, the computations for multiplication rule can be carried out as

P (A and B) = P(A) * P(B|A) or P(B) * P(A|B)

P = P(tails) * P(heads) = (0.5) * (0.5) = 0.25

Rule of complement:

As before, the rule of supplement may also be considered the rule of subtraction. The mutually exclusive character of P(A) and P (not A) forms the basis of this rule. This rule implies that two occurrences can never happen simultaneously, yet one must always happen.

If a weather forecast tells, for instance, that tomorrow has 0.6 probability of rain, what is the probability of no rain then? To calculate such probability, the formula used is P (not A) = 1 – P(A).

Probability Theory

Probability theory is the field of mathematics that deals with likelihood of events occurrences. While many diverse interpretations of probability exist, probability theory precisely defines the notion through a series of hypotheses and axioms.

The hypotheses assist to create a probability in terms of a space for possible measurements between 0 and 1. This is referred to as the probability measure to a number of possible sample space outcomes.

Note: There is a little bit confusion between the concept of probability and expected value. Since probability is the number of possible ways to occur in any event while the expected value is the prediction of any event in future. One may also use expected value calculator for online prediction. It also provides a best difference between two main concepts of probability and expected value. If you visit this site you will find a lot of information about technology

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