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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
)
Probability ↓↑ - Previous
What is Probability
Next - Probability ↓↑
Marginal Probability
Last modified
9mo ago
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