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joint probability
What is joint probability? Explain with example.
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Joint probability
It is a type of probability that interpreters use to determine the chances of happening two things together at the same time. In simple terms, it means that we calculate the probability of a particular Event A, that is occurring at the same time as Event B.
In the mathematical term: “Joint probability is the probability of two events that are occurring together.”
It can also be further defined as the intersection of two or more events in terms of sets.
The use of joint probability is mainly for the analysts and statisticians who need to take into account both events occurring at the same time.
But we cannot use this to estimate and find out whether an event can occur in the presence or influence of another event.
Joint probability: Mathematical Discussion
Statistically, the joint probability of two events, which can be A and B, is written mathematically as P(A, B).
How to get this? We need to simply multiply the probability of Event Y and the probability of Event Z together.
Example:
Give the probability that number 3 will occur twice simultaneously when two distinct dices are rolled.
Solution:
Therefore, each die contains six possible numbers. Therefore, the probability of occurring three in a die is one-sixth or in decimal, it is equal to 0.1666. If we name the dice A and B. Therefore, the probabilities from each dice are as followed:
P(A) = 0.1666
P(B) = 0.1666
(Where P = Probability)
Therefore to calculate the final probability, we need om to multiply the probabilities of occurring three in the dices. They are 0.1666 as calculated earlier.
So the final probability of the problem is calculated as:
P(A,B) = 0.1666 x 0.1666 = 0.02777
Hence, the joint probability to get two threes while rolling two dices simultaneously gives is 0.02777.
