Question

state and prove addition theorem on probability

Answer 1

The addition rule is a result used to determine the probability that event A or event B occurs or both occur. 

The result is often written as follows, using set notation: 
P(A U B) = P(A) + P(B) - P(P int B) 

where: 
P(A) = probability that event A occurs 
P(B) = probability that event B occurs 
P(A U B) = probability that event A or event B occurs 
P(A int B) = probability that event A and event B both occur 

Proof: 

For mutually exclusive events, that is events which cannot occur together: P(A int B) = 0 
The addition rule therefore reduces to 
P(A U B)= P(A) + P(B) 

For independent events, that is events which have no influence on each other: 
P(A int B) = P(A).P(B) 
The addition rule therefore reduces to 
P(AUB)=P(A)+P(B)-P(A).P(B) 

In both cases the rules stands true. 

This can also be proved with venn diagram. 

I hope I answered your question. 

Answer 2

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The addition rule is a result used to determine the probability that event A or event B occurs or both occur. 

The result is often written as follows, using set notation: 

P(A U B) = P(A) + P(B) - P(P int B) 

where: 

P(A) = probability that event A occurs 

P(B) = probability that event B occurs 

P(A U B) = probability that event A or event B occurs 

P(A int B) = probability that event A and event B both occur 

Proof: 

For mutually exclusive events, that is events which cannot occur together: P(A int B) = 0 

The addition rule therefore reduces to 

P(A U B)= P(A) + P(B) 

For independent events, that is events which have no influence on each other: 

P(A int B) = P(A).P(B) 

The addition rule therefore reduces to 

P(AUB)=P(A)+P(B)-P(A).P(B) 

In both cases the rules stands true. 

This can also be proved with venn diagram. 

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