Probability

Introduction

Randomness can be found everywhere. The study of Probability theory refers to the “mathematical framework” that is used in order to analyze the chance of an event that is going to occur. Sometimes it is very difficult to predict the occurrence of an event. In that case, it is possible to predict the likeliness of the event that will occur or will not occur with the application of Probability.

What is Probability?

The term “Probability” refers to the “ratio of the number” of outcomes that is favorable to the “total number of outcomes” that can happen in the event. For example, if in an event there are “n” number of possible outcomes from a performed experiment and number of favorable outcomes from the experiment are “y”. Then the “Probability” or chances that the outcome from the event will be favorable can be expressed as

Probability(event)= number of favorable outcomes/number of possible outcomes from a performed experiment = y/n

Properties of Probability

• The “probability” of an “event that is certain” or sure is 1

• The “probability” of an event that is impossible or not occurring is Zero or 0
• The value of the “Probability” of an event ranges from 0 to 1. It can be expressed in mathematical expression as 

0 <= Probability of the event <= 1

• In the case of “event A” and “event B” are “two mutually exclusive events” then the probability of “P(AUB)= P(A) + P(B)

“Mutually exclusive events” refers to the events that cannot happen simultaneously. For example, the “probability” of getting “Head or Tail when a coin is tossed.

• The events that are associated with an experiment can be referred to as “atomic events or Sample points or Elementary events”. The summation of the probability of all the elementary events of an event is 1. For example, the “Elementary event” of a tossed coin is getting a Head or Tail. The summation of the probability of P(H) and P(T) is 1.
• The summation of the probability of “Complementary event” is 1.

P(H) + P(H’) = 1

• In case of the events that are “not mutually exclusive,” the probabilities can be expressed as,

P(AUB) = P(A) + P(B) – P(A∩B)

P(A∩B) = P(A) + P(B) – P(AUB)

• If there are “n” number of “mutually exclusive events” then the “Probability” can be expressed as,

P(E1UE2UE3…….En) = P(E1) + P(E2) + P(E3) + …….  P(n)

Types of Probability

There are various  types of probability that are used to predict the possibilities of the occurring of the events and they are discussed as

Classical or Theoretical

This perspective of the probability states that, If in an event there are “X outcomes” that are “equally likely”and “event Y” has exact “Z” outcomes, then it can be said that the “Probability”  of Y is Z/X” or “P(Y) = Z/X”. This is generally taught to the student at a lower level. Consider an example of “rolling a dice”, each of the outcomes has equal chances after a dice is rolled. Getting 1 has a probability of 1/6  and is the same for all other outcomes that can be obtained from rolling dice. Another example can be considered, “Card Probability” which is drawing a card from a deck of cards, probability of getting each of the cards from the deck is 1/52 and is equal for all the cards in the deck when the card is drawn randomly from the deck.

Empirical or Experimental

This perspective of “probability” can be defined as “Probability through experiments.” In the case of a die with the difference in the distribution of weight, it is not possible to predict the possibilities or “probability” of the event, it is possible to estimate the probability of the occurrence based on the outcome of the rolled die. 

Subjective

This perspective of the “probability” is based on the personal belief of an individual, for example, it is possible for someone to estimate the probability of win or loss of a football team based on the past record of “winning and loses” of the team or opinion of the “match analyser”. Basically “Subjective probability” is the estimation of the “likeliness of an event to occur” based on the knowledge of the individual.

Conditional Probability

“Conditional probability” can be referred to as the chances of the “occurrence of an event”, based on the event that has already occurred in the past. For example, Consider two events A and B. Event B can only occur after it is found out that Event A has occurred. Then the “Conditional Probability” of “event A” and “event B” is the multiplication of the probability of A and B.

Conclusion

This article includes a meta description of the “Probability” in order to have a better understanding of the probability. This article discusses the idea of the “probability” that is used to understand the possibilities of the occurrence of an event. This article also includes the “Properties of probability”. Various types of probability are also discussed in this article. The probabilities that are discussed in this article are “Classical or theoretical probability, Empirical or Experimental probability, Subjective probability and Conditional probability”. The frequently asked question answer associated with probability is also discussed in this article.