In this post, you will learn about joint and conditional probability differences and examples. When starting with Bayesian analytics, it is very important to have a good understanding around probability concepts. And, the probability concepts such as joint and conditional probability is fundamental to probability and key to Bayesian modeling in machine learning. As a data scientist, you must get a good understanding of probability related concepts.
In this section, you will learn about basic concepts in relation to Joint and conditional probability.
Probability of an event can be quantified as a function of uncertainty of whether that event will occur or not. Let’s say an event A is whether rolling a die will result in 2. You may want to know about the uncertainty related to whether event A will occur or not. This can also be stated as what is the probability that the event A will occur. Mathematically, probability of whether event A will occur or not can be denoted as P(A).
When we talk about two events, then the concept of joint and conditional probability comes into picture. Taking the rolling die as example, let’s consider another event B such as whether rolling a die will result in one of the event numbers such as 2, 4 or 6. The probability of an event B occurring can be denoted as P(B).
Conditional probability is probability of an event given that another event has occurred. Going by the example sighted above, conditional probability in terms of event A and B can be defined as probability of event A (rolling a die results in 2) given event B (rolling the die result in even number 2, 4 or 6) has occurred. Mathematically, it can be written as P(A | B).
Joint probability of two events A and B is termed as the product rule of probability and can be represented mathematically as the following:
P(A, B) = P(A | B) * P(B)
The above can be read as the following:
Joint probability P(A, B) of event A and B is the product of probability of event A given event B occurred and the probability of event B. Going by the rolling die example, joint probability of event A (rolling die results in 2) and event B (rolling die results in an even number) is product of probability of event A (rolling die results in 2) given event B (rolling die resulted in even number) and probability event B (rolling die resulted in the even no.)
Here are some examples of joint and conditional probability:
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