Joint Probability

What Is a Joint Probability?

Joint likelihood is a statistical measure that works out the probability of two events happening together and at a similar point in time. Joint likelihood is the likelihood of event Y happening while event X happens.

The Formula for Joint Probability Is

Documentation for joint likelihood can take a couple forms. The accompanying formula addresses the likelihood of events crossing point:
$\begin & P\ \left ( X\bigcap Y \right ) \ &\textbf\ &X, Y = \text\ &P(X \text Y), P(XY) = \text\ \end$

What Does Joint Probability Tell You?

Likelihood is a field closely connected with statistics that arrangements with the probability of an event or peculiarities happening. It is evaluated as a number somewhere in the range of 0 and 1 comprehensive, where 0 shows a unimaginable chance of occurrence and 1 signifies the certain outcome of an event.

For instance, the likelihood of drawing a red card from a deck of cards is 1/2 = 0.5. This means that there is an equivalent chance of drawing a red and drawing a black; since there are 52 cards in a deck, of which 26 are red and 26 are black, there is a 50-50 likelihood of drawing a red card versus a black card.

Joint likelihood is a measure of two events occurring simultaneously, and must be applied to circumstances where beyond what one perception can happen simultaneously. For instance, from a deck of 52 cards, the joint likelihood of picking up a card that is both red and 6 is P(6 ∩ red) = 2/52 = 1/26, since a deck of cards has two red sixes — the six of hearts and the six of diamonds. Since the events "6" and "red" are independent in this model, you can likewise utilize the accompanying formula to ascertain the joint likelihood:
$P(6 \cap red) = P(6) \times P(red) = 4/52 \times 26/52 = 1/26$
The symbol "∩" in a joint likelihood is referred to as a convergence. The likelihood of event X and event Y happening is exactly the same thing as the point where X and Y cross. In this manner, joint likelihood is additionally called the crossing point of at least two events. A Venn diagram is maybe the best visual instrument to make sense of a crossing point:

From the Venn over, the point where the two circles overlap is the convergence, which has two perceptions: the six of hearts and the six of diamonds.

The Difference Between Joint Probability and Conditional Probability

Joint likelihood ought not be mistaken for conditional probability, which is the likelihood that one event will happen given that another action or event occurs. The conditional likelihood formula is as per the following:
$P(X, given~Y) \text P(X | Y)$
This is to say that the chance of one event happening is conditional on another event occurring. For instance, from a deck of cards, the likelihood that you get a six, given that you drew a red card is P(6│red) = 2/26 = 1/13, since there are two sixes out of 26 red cards.

Joint likelihood just factors the probability of the two events happening. Conditional likelihood can be utilized to compute joint likelihood, as found in this formula:
$P(X \cap Y) = P(X|Y) \times P(Y)$
The likelihood that An and B happens is the likelihood of X happening, given that Y happens increased by the likelihood that Y happens. Given this formula, the likelihood of drawing a 6 and a red simultaneously will be as per the following:
$\begin &P(6 \cap red) = P(6|red) \times P(red) = \ &1/13 \times 26/52 = 1/13 \times 1/2 = 1/26\ \end$
Analysts and analysts utilize joint likelihood as a device when at least two perceptible events can happen all the while. For example, joint likelihood can be utilized to estimate the probability of a drop in the Dow Jones Industrial Average (DJIA) joined by a drop in Microsoft's share price, or the chance that the value of oil ascends simultaneously the [U.S. dollar weakens](/powerless dollar).