Previously we have discussed about first order differential equation and In today's session we are going to discuss about Addition Theorem in probability which is a part of cbse books for class 11, In mathematics, probability can be considering as a branch of mathematics which is popularly used for estimating the likelihood occurrence any particular event. Basically the concept of probability is used for predict the output of any particular event which are performed again and again. The probability is a mathematical term which can be express between the ranges from 0 to 1. if in case the probability of an event contains the value o then we can say that the possibility of that event is impossible to done. In the same aspect if probability of an event is 1 then we can say that the event is in a certain status. An event with a probability of .5 can be considered to have equal odds of occurring or not occurring.

Here we are going to discussing about the addition theorem in probability. According to the Addition theorem of probability, the probability of an event x and y can be determine by the probability that event A or event B occurs or both occur. In the simple mean we Define Addition Theorem as for any two events like

 x and y the probability of x union y is equals to the probability of x added to probability of y then minus the probability of x intersection y from them.

P (x ∪y) = P( x ) + P( y ) - P(x ∩ y )

The above notation Define Addition Theorem in the form of mathematical notation: P(x ) = It describe the probability of an event x occurs.

P(y) = It describe the probability of an event y occurs.

P(x U y ) =  it describe the probability that event x or event y occurs. P(x ∩ y )= it describe the probability that event x or event y occurs. The addition theorem probability can be proved by the following process, which are given as: For mutual exclusive events, the events which cannot occur together: P(x ∩ y )= 0  The addition rule therefore reduces to P(x U y ) = P( x ) + P( y )

On the other side for any independent events, which have no influence on each other 

P(x ∩ y )= P( x ) *P( y ) The addition rule therefore reduces to  P(x U y )=P( x ) + P( y ) - = P( x ) *P( y )

In both situations it will give the same output.