what does joint probability tell you 
probability is a field closely related to statistics that deals with the likelihood of an event or phenomenon occurring it is quantified as a number between 0 and 1 where 0 indicates an impossible chance of occurrence 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 there is an equal chance of drawing a red and black card since there are 26 of each in a deck as such there is a 50 50 probability of drawing a red card versus a black card joint probability measures two events that happen at the same time it can only be applied to situations where more than one observation can occur at the same time so the joint probability of picking a card that is both red and 6 from a deck 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 because the events red and 6 are independent you can also use the following formula to calculate the joint probability p 6 r e d p 6 p r e d 4 52 26 52 1 26 p 6 cap red p 6 times p red 4 52 times 26 52 1 26 p 6 red p 6 p red 4 52 26 52 1 26the symbol in a joint probability is referred to as an intersection the probability of event x and event y happening is the same thing 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 from the venn above the point where both circles overlap is the intersection which has two observations the six of hearts and the six of diamonds joint probability vs conditional probabilityjoint probability should not be confused with conditional probability which is the probability that one event will happen given that another action or event happens the conditional probability formula is as follows p x g i v e n y or p x y p x given y text or p x y p x given y or p x y this is to say that the chance of one event happening is conditional on another event happening for example from a deck of cards the probability 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 probability only factors in the likelihood of both events occurring conditional probability can be used to calculate joint probability as seen in this formula p x y p x y p y p x cap y p x y times p y p x y p x y p y the probability that a and b occurs is the probability of x occurring given that 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 6 r e d p 6 r e d p r e d 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 p 6 red p 6 red p red 1 13 26 52 1 13 1 2 1 26 statisticians and analysts use joint probability as a tool when two or more observable events can occur simultaneously for instance joint probability can be used to estimate the likelihood of a drop in the dow jones industrial average djia accompanied by a drop in microsoft s share price or the chance that the value of oil rises at the same time the u s dollar weakens joint probability depends on the two events acting independently from one another to determine whether they are truly independent it s important to establish whether one s outcome affects the other if they do they are dependent which means they lead to conditional probability if they don t you end up with joint probability example of joint probabilitylet s highlight another example to show how joint probability works this example uses dice and we want to find out what the probability is that you ll roll a four on each die when you roll them remember there are six sides to each one in order to determine the joint probability we first need to determine the probability of each roll now we can use the joint probability formula noted above to figure out what the joint probability is for this event by multiplying each individual event together 1 6 x 1 6 1 36this means that there is a 1 36 chance of rolling two fours using a pair of dice 