Question

State and prove the law of addition for two events.​

Answer 1

A and B are any two events then the probability of happening of at least one of the events is defined as P(AUB) = P(A) + P(B)- P(A∩B).

Proof:

Since events are nothing but sets,

From set theory, we have

n(AUB) = n(A) + n(B)- n(A∩B).

Dividing the above equation by n(S), (where S is the sample space)

n(AUB)/ n(S) = n(A)/ n(S) + n(B)/ n(S)- n(A∩B)/ n(S)

Then by the definition of probability,

P(AUB) = P(A) + P(B)- P(A∩B).

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Answer 2

Answer:

Addition theorem of probability → If A and B are any two events then the probability of happening of at least one of the events is defined as

P(A∪B)=P(A)+P(B)−P(A∩B)

Proof:-

From set theory, we know that,

n(A∪B)=n(A)+n(B)−n(A∩B)

Dividing the above equation by n(S) both sides we have

n(S)

n(A∪B) = n(S)n(A) +n(S)n(B) − n(S)n(A∩B)

P(A∪B)=P(A)+P(B)−P(A∩B)(∵P(X)= n(S)n(X)

Explanation:

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