Joint Probability

Joint probability is the probability of two events happening together.
The two events are usually designated event A and event B. In probability terminology, it can be written as:
P(A∩B)=P(A,B)=P(A∣B)∗P(B)P(A \cap B) =P(A,B) = P(A|B)*P(B)P(A∩B)=P(A,B)=P(A∣B)∗P(B)
Anyway, if an event A and B are idenpendent then P(A∣B)=P(A)P(A|B) = P(A)P(A∣B)=P(A), and therefore, P(A∩B)=P(A,B)P(A \cap B) = P(A,B) P(A∩B)=P(A,B) become P(A)∗P(B)P(A) * P(B)P(A)∗P(B) 
Example: The probability that a card is a five and black = p(five and black) 
2/52 = 1/26
(There are two black fives in a deck of 52 cards, the five of spades and the five of clubs).
OR Events
P(A∪B)=P(A)+P(B)−P(A∩B)P(A \cup B) = P(A)+P(B)-P(A \cap B)P(A∪B)=P(A)+P(B)−P(A∩B)

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