Conditional Probability

 The concept of conditional probability is based on the concept of independent and dependent events.  It is described as the possibility of a result or an outcome that is dependent on the previous result or outcome. It can be calculated by multiplying the probability of the previous with the renewed outcome which is the conditional event.

The probability of occurring of event A which is dependent on the outcome of event B i.e. outcome of an event is conditioned on the outcome of another event, is known as conditional probability. 

Conditional Probability Formula

Let us assume two events A and B and the outcome of B is dependent on A. Them, the conditional probability formula is-

P(B|A) = P(A∩B) / P(A)

Conditional Probability Checker

A conditional Probability checker refers to an online tool that is used to calculate conditional probability. It first provides the probability of the first event and then the second event that is happening. The tool is used so that the user doesn’t have to perform that manually.

Conditional Probability vs. Joint Probability

Conditional probability: P(E|F) is the probability of event E happening, which is conditioned on the outcome of the event of F. For example, given that a red card is drawn. The probability that it is a four (p(four|red)) = 2/26= 1/13.

 Joint Probability: The probability of event E and event Foccurring. It is the probability of the intersection of two or more events. The probability of the intersection of E and F may be written P(E ∩ F). Example: the probability that a card is a three and green =p(three and green) = 2/52=1/26. (There are two green fours in a deck of 52, the 4 of hearts and the 4 of diamonds).

Bayer’s Theorem

The theorem states the probability of the outcome of the event which is related to a condition. It is only used in the case of conditional probability. 

P(A|B) = {P(B|A) P(A)}/ P(B)

Properties

Property 1: Let A and B are the events with a sample space of S , then-

P(A|B)= P(B|B) = 1

Property 2: If E and F are any two events with a sample space S and G is an event of S so that P(G) ≠ 0, then-

((E ∪ F)|G) = P(E|G) + P(F|G) – P((E ∩ F)|G)

Property 3: P(A′|B) = 1 − P(A|B)

Prior Probability:

Prior probability refers to the probability of an event that is happening before any data or information is present which can be used to determine the probability. The probability is calculated by a prior belief.

Compound probability:

This probability is used to express the likelihood of events independent of each other. It is calculated by multiplying the first event with the second event. 

Conclusion: 

It is easy to calculate the probability of an event happening from its definition. But finding the probability of an event when it is conditioned on the outcome of another event is difficult. Here comes conditional probability. The concept of conditional probability is based on the concept of independent and dependent events. A conditional Probability checker refers to an online tool that is used to calculate conditional probability.