Machine Learning - Probability and Counting Rules - The Addition Rules for Probability

The addition rules for probability

Two events are mutually exclusive events. If they cannot occur at the same time, that is, they have no outcomes in common, then

we can use this addition rules for probability. So this addition rules for probability will be applicable between two events when they are

mutually exclusive events. Let us go for one example. A single die is rolled, getting an odd number and getting an event number in the outcome

So, they are obviously mutually exclusive. So when two events A and B are mutually exclusive, the probability that A or B will be

occurring in this way, will be calculated in this way, that is probability of event A or

even B is equal to probability of A plus probability of B. Let us go for a

one example. A box contains three red balls, four blue balls and five green balls. If a person

selects a ball at random, find the probability that it is either a red ball or a green ball

So, since the box contains three red balls, four blue balls and five green balls, so a total

of 12 balls, that means three plus four, seven plus five, that is 12. So, probability of red

or green balls will be the probability of red balls plus probability of green balls

In the previous slide also we have discussed that one, probability of event A or event B is

equal to probability of A plus probability of B. So, this is known as the addition rule for

probability So here in this case we having this 3 by 12 plus 5 by 12 is equal to 8 by 12 is equal to 2 by 3 So here the events are mutually exclusive because at the same time a ball cannot be

of type red or green simultaneously. If A and B are not mutually exclusive, then the respective formula will be probability of

A or B is equal to probability of A plus probability of event B minus probability of A and B

So, here we are having one respective table. You can find that out of this eight nurses we are having seven female and one male

Out of say five physicians, we are having three female physicians and two male physicians

So how many female staffs are there? many male staffs are there, how many nurses, how many physicians, we have also done the calculation

And this is the total number of stops we have considered here

Now the probability is nurse or male. Nars or male. But we are having some nurses who are also male

So that's why we are having, they are not mutually exclusive, we are having some common

So in that case how to calculate? There is a probability of nurse plus probability of male or male

minus probability of male nurse. So that is 8 by 13. You can easily see that 8 by 13

That is a probability of nars out of 13 stops. Probability of male

So probability of male means this one. So 3 by 13 minus we are having only one male nurse

So minus 1 by 13. So the probability will be 10 by 13

So in this way, in this video, we have discussed that is the addition rules for probability

calculation. Thanks for watching this video