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Probability is the likelihood of something happening. It is an essential part of mathematics. Probability theories are crucial segments for competitive exams. Many questions come from this section for GATE exams. Conditional probability is a type of probability. Conditional probability provides the likelihood of things or events happening but is based on previous data. This data is obtained through repeated occurrences of a particular event and observations. It also stipulates that the chances of Y occurring are directly dependent on the instances of X happening before. It is therefore represented as: P (X|Y) = P (X sigma Y) / P(Y).

Conditional Probability

The conditional probability, therefore, relies on previous occurrences of an event. Conditional probability explains the possible links between an event X and an event Y. Conditional probability provides the likelihood of things or events happening but is based on previous data. Conditional probability relies on an event that has happened before. If two unlikely events are considered for the calculations of conditional probability then it creates fallacies. There are certain traits of conditional probability:

  • There must be some similarity shared between the previous event and the present event
  • The value of unconditional probability is always more than 0 (P (y) > 0)
  • Event X must have every outcome considered
  • Conditional probability is based on intersections of the two events and their possible outcomes

Computing probabilities necessitates conditional probabilities. Many scientists have seen and interpreted this function variously. Some have preferred to interpret conditional probability as a probability axiom.

Conditional Probability Formula

The conditional probability formula provides the likelihood of things or events happening but is based on previous data. This data is obtained through repeated occurrences of a particular event and observations. It also stipulates that the chances of Y occurring are directly dependent on the instances of X happening before. The conditional probability formula is therefore represented as: P (X|Y) = P (X sigma Y) / P(Y). The understanding of conditional probability and the variations in the formula depend on its interpretations:

  • Partially conditional- In this conditional probability formula, the equation is:

(X|Y1 = y1 …. ym = ym). It states that possible outcomes of X have happened to some degree but it is not all.

  • Zero Probability- In this conditional probability formula, the equation is represented as:

P|Y = 0 then P (X|Y) not defined.

  • Conditional Event- here, the conditional probability formula is represented as:

P (Xy) = P (X sigma Y) / P (Y).

  • Discrete Variables- The conditional probability formula for this one is:

P (X|V = y)

Conditional Probability Examples

Conditional Probability examples are important for students to learn conditional probabilities. Conditional probabilities form a considerable area of questions appearing for exams. In competitive exams like GATE, studying conditional probability examples is beneficial. Conditional probability examples are a part of mathematics and statistics. A few conditional probability examples have been provided here:

  • There are 100 units of toys. 40 has red lights on them, 30 has fancy decorations and 20 of them have both of the features. If someone buys a toy randomly then how likely is it that they bought the one with fancy decorations?

Solution: P (X) is 0.4% from the 40.

So, P (X sigma Y) / P(Y) is 20 or 0.2%.

  • There are 26 Pokémon cards. There is a Charizard card. What is the probability of drawing a 4charzard card?

Solution: The probability is 0.5.

Conditional Probability Equation

While concentrating on conditional probability looking at conditional probability equation is also important. The conditional probability equation is as follows:

P (X|Y) = P (X sigma Y) / P(Y).

Computing probabilities necessitates conditional probabilities. Many scientists have seen and interpreted this function variously.

Conclusion

Computing probabilities necessitates conditional probabilities. Many scientists have seen and interpreted this function variously. Some have preferred to interpret conditional probability as a probability axiom. Conditional probabilities form a considerable area of questions appearing for exams. Conditional probability examples are a part of mathematics and statistics. It is an essential part of mathematics. Probability theories are crucial segments for competitive exams. Many questions come from this section for GATE exams. Conditional probability is a type of probability.