Зміст курсу
Probability Theory Basics
5. Covariance and Correlation
Probability Theory Basics
The Multiplication Rule of Probability
We have already considered that if events A and B are independent, then:P(A and B) = P(A) *P(B)
.
This formula is a special case of the more general probabilities multiplication rule:
It states that the probability of the joint occurrence of two events, A and B, is equal to the probability of event A multiplied by event B's conditional probability, given that event A has occurred.
Example
Assume you draw two cards from a standard deck (52 cards) without replacement. What is the probability of drawing a heart on the first card and a diamond on the second?
Event A - drawing a heart first.
Event B - drawing a diamond second.
Note
Pay attention that in the multiplication probabilities rule, the order in which events occur is unimportant - we can consider both the probability
P(B)*P(A|B)
andP(A)*P(B|A)
.
Все було зрозуміло?
Зміст курсу
Probability Theory Basics
5. Covariance and Correlation
Probability Theory Basics
The Multiplication Rule of Probability
We have already considered that if events A and B are independent, then:P(A and B) = P(A) *P(B)
.
This formula is a special case of the more general probabilities multiplication rule:
It states that the probability of the joint occurrence of two events, A and B, is equal to the probability of event A multiplied by event B's conditional probability, given that event A has occurred.
Example
Assume you draw two cards from a standard deck (52 cards) without replacement. What is the probability of drawing a heart on the first card and a diamond on the second?
Event A - drawing a heart first.
Event B - drawing a diamond second.
Note
Pay attention that in the multiplication probabilities rule, the order in which events occur is unimportant - we can consider both the probability
P(B)*P(A|B)
andP(A)*P(B|A)
.
Все було зрозуміло?