Joint Probability Definition


What is a joint probability?

Joint probability is a statistical measure that calculates the probability that two events will occur together and at the same time. The joint probability is the probability that the event Y occurs at the same time as the event X occurs.

The formula for common probability is

Scoring the joint probability can take many different forms. The following formula represents the probability of intersection of events:


P (XYes)or:X,Yes=Two different events that intersectP(X and Yes),P(XYes)=The joint probability of X and Y begin {aligned} & P left (X bigcap Y right) \ & textbf {where:} \ & X, Y = text {Two different intersecting events} \ & P (X text {and} Y), P (XY) = text {The joint probability of X and Y} \ end {aligned}

TheP (XYes)or:X,Yes=Two different events that intersectP(X and Yes),P(XYes)=The joint probability of X and YTheThe

What does the joint probability tell you?

Probability is a statistical domain that deals with the probability that an event or phenomenon will occur. It is quantified as a number between 0 and 1 inclusive, where 0 indicates an impossible chance of occurring and 1 denotes the certain outcome of an event.

For example, the probability of drawing a red card from a deck of cards is 1/2 = 0.5. This means that there is an equal chance of drawing a red and drawing a black; Since there are 52 cards in a deck, including 26 red and 26 black, there is a 50-50 probability of drawing a red card against a black card.

Joint probability is a measure of two events occurring at the same time and can only be applied to situations where several observations can occur at the same time. For example, in a deck of 52 cards, the common probability of taking one card that is both red and 6 is P (6 ∩ red) = 2/52 = 1/26, because a card game has two six reds. the six of hearts and the six of diamonds. You can also use the following formula to calculate the joint probability:


P(6rere)=P(6)×P(rere)=4/52×26/52=1/26P (6 red cap) = P (6) times P (red) = 4/52 times 26/52 = 1/26


The symbol “∩” in a joint probability is called an intersection. The probability that event X and event Y occur is the same as the point where X and Y intersect. Therefore, the joint probability is also called the intersection of two or more events. A Venn diagram is perhaps the best visual tool to explain an intersection:

Image of Julie Bang © Investopedia 2019

From the Venn above, the point where the two circles overlap is the intersection, which has two observations: the six of hearts and the six of diamonds.

The difference between the joint probability and the conditional probability

The joint probability should not be confused with the conditional probability, which is the probability that an event will occur given that another action or event occurs. The conditional probability formula is as follows:


P(X,gIvenot Yes) or P(X|Yes)P (X, given ~ Y) text {or} P (X | Y)

P(X,gIvenot Yes) or P(X|Yes)The

This means that the probability of one event occurring is conditional on another event occurring. For example, from a deck of cards, the probability that you will get a six, since you have drawn a red card is P (6│red) = 2/26 = 1/13, because there are two six out of 26 red cards.

The joint probability only takes into account the probability that the two events will occur. The conditional probability can be used to calculate the joint probability, as this formula shows:


P(XYes)=P(X|Yes)×P(Yes)P (X cap Y) = P (X | Y) times P (Y)


The probability that A and B will occur is the probability that X will occur, since Y occurs multiplied by the probability that Y occurs. Given this formula, the probability of drawing a 6 and a red at the same time will be as follows:


P(6rere)=P(6|rere)×P(rere)=1/13×26/52=1/13×1/2=1/26 begin {aligned} & P (6 cap red) = P (6 | red) times P (red) = \ & 1/13 times 26/52 = 1/13 times 1/2 = 1 / 26 end {aligned}


Statisticians and analysts use joint probability as a tool when two or more observable events can occur simultaneously. For example, the joint probability can be used to estimate the probability of a decline in the Dow Jones Industrial Average (DJIA) accompanied by a fall in Microsoft’s stock price, or the possibility that the value of oil will increase at the same time. while the US dollar weakens.

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