PPT - Conditional probability | SSC CGL Tier 2 - Study Material, Online Tests, Previous Year PDF Download

 Page 1


Probability 
Conditional Probability  
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Probability 
Conditional Probability  
Conditional Probability
? When we want the probability of an event from a 
conditional distribution, we write P(B|A) and 
pronounce it “the probability of B given A.”
? A probability that takes into account a given 
condition is called a conditional probability.
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Probability 
Conditional Probability  
Conditional Probability
? When we want the probability of an event from a 
conditional distribution, we write P(B|A) and 
pronounce it “the probability of B given A.”
? A probability that takes into account a given 
condition is called a conditional probability.
Conditional Probability (cont.)
? To find the probability of the event B given the 
event A, we restrict our attention to the outcomes 
in A. We then find in what fraction of those
outcomes B also occurred.
? Note: P(A) cannot equal 0, since we know that A
has occurred.
(A and B)
( | )
()
P
P
P
? BA
A
Page 4


Probability 
Conditional Probability  
Conditional Probability
? When we want the probability of an event from a 
conditional distribution, we write P(B|A) and 
pronounce it “the probability of B given A.”
? A probability that takes into account a given 
condition is called a conditional probability.
Conditional Probability (cont.)
? To find the probability of the event B given the 
event A, we restrict our attention to the outcomes 
in A. We then find in what fraction of those
outcomes B also occurred.
? Note: P(A) cannot equal 0, since we know that A
has occurred.
(A and B)
( | )
()
P
P
P
? BA
A
Independence
? Independence of two events means that the 
outcome of one event does not influence the 
probability of the other.
? With our new notation for conditional 
probabilities, we can now formalize this definition:
? Events A and B are independent whenever 
P(B|A) = P(B). (Equivalently, events A and B
are independent whenever P(A|B) = P(A).) 
Page 5


Probability 
Conditional Probability  
Conditional Probability
? When we want the probability of an event from a 
conditional distribution, we write P(B|A) and 
pronounce it “the probability of B given A.”
? A probability that takes into account a given 
condition is called a conditional probability.
Conditional Probability (cont.)
? To find the probability of the event B given the 
event A, we restrict our attention to the outcomes 
in A. We then find in what fraction of those
outcomes B also occurred.
? Note: P(A) cannot equal 0, since we know that A
has occurred.
(A and B)
( | )
()
P
P
P
? BA
A
Independence
? Independence of two events means that the 
outcome of one event does not influence the 
probability of the other.
? With our new notation for conditional 
probabilities, we can now formalize this definition:
? Events A and B are independent whenever 
P(B|A) = P(B). (Equivalently, events A and B
are independent whenever P(A|B) = P(A).) 
The General Multiplication Rule
? When two events A and B are independent, we 
can use the multiplication rule for independent 
events : 
P(A and B) = P(A) x P(B)
? However, when our events are not independent, 
this earlier multiplication rule does not work. 
Thus, we need the General Multiplication Rule.