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In this class, we discuss the Mathematics Basics Required for Naive Bayes.
Dependent events, Independent events, Conditional probability, Bayes Theorem.

The above are the Mathematics Basics Required for Naive Bayes.

Independent events:

Two events are said to be independent if one event occurrence does not affect the probability of another event.

An example is tossing a coin twice.

Let's toss a coin and the probability of occurring event head is 1/2.

If we toss the coin second time the probability of occurring event head is 1/2.

One event does not affect the probability of another event.

The probability of occurring both the events is given as P A and B = p A P B .

Dependent Events:

One event occurrence is affecting the probability of another event They are dependent events.

Example take a deck of playing cards.

In the deck, we have 52 cards.

Two events are picking two cards randomly.

What is the probability of picking the first card Ace and Second card Ace?

Total four Ace cards in 52 cards.

The probability of picking ace first time is 4/52.

The probability of picking ace second time is 3/51.

After picking ace the first time we have only 51 cards left.

So the probability of one event affecting the output of the second event.

It is given p of A and B = P of A P of B|A

P of B|A means conditional probability.

Conditional probability:

Probability of an event to occur if already an event occurred.

Example Rolling 2 dice. it was given one dice shown 2.

What is the probability of the sum of values on two dice greater than 6?

It was given event A has occurred ie One dice showed 2.

The new sample size is 2,1 2,2 2,3 2,4 2,5 2,6.

Out of these six events greater than six are 2 events.

2,5 and 2,6 so the probability of event B occurred is 2/6.

P of B|A = 2/6.

PB|A = PA and B/PA.

Bayes theorem:

It was given conditional probability as PB|A = P of A and B/Pof A.

P of A|B = P of A and B/P of B.

Take P of A and B = P of A|B P of B

Substitute this equation in the above equation

P of B|A   =  P of A|B P of B /P of A. This is Bayes equation.

Importance: if p of B|A is known we can find easily P of A|B by using the Bayes equation.



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