Probability and Information Theory - Lecture 2 Part 2

[Applause] okay so uh as I told you last time um there is a lot of uh intuition that we can build by studying uh prototype problems in probability Theory and uh and also many uh problems that we might be interested in can be reduced uh to uh studying one of these uh problems so we have already seen uh that uh one class of problems of this type are problems okay so um so the next thing I want to discuss is another very useful um formula uh that uh is very useful to compute complicated um questions okay so and uh uh so what you have seen is that if you have uh two events if you have two events A and B then the probability of the Union that is the probability of a plus the probability of B minus the probability of the intersection okay so what happens uh if I introduce if I want to compute uh uh the probability one one of three events occur either a or b or c occurs okay so um so for this uh essentially we need we can generalize this so so imagine that we have a SE of events of n event s and then we want to define the event which is the union of this which is the event that at least this this this sum here will be limited uh from one to M okay and then uh in this um um if this um um so if uh uh if no is less than less or equal to M so the if this Omega belongs to this event then this will contribute by one otherwise it will contribute by zero and how in how many combination of this uh how many possible uh in how many evidence of this sum and how many terms of this sum will this occur well this will occur just in M choose no um um in M uh choose no of these STS okay so uh if you look at uh if you look at this equation this is the bomal expansion apart from the fact that there is a one here and there is a plus one here so this is one minus