Question

what is the formula of bayes theorem and explain it with an example
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Answer 1

what is the formula of bayes theorem and explain it with an example

Answer 2

Answer:

Bayes Theorem is a way of finding probability when we know certain other probabilities.

Step-by-step explanation:

The formula is:

P(A|B) =  P(A) P(B|A)P(B)

Which tells us:   how often A happens given that B happens, written P(A|B),

When we know:   how often B happens given that A happens, written P(B|A)

   and how likely A is on its own, written P(A)

   and how likely B is on its own, written P(B)

Let us say P(Fire) means how often there is fire, and P(Smoke) means how often we see smoke, then:

P(Fire|Smoke) means how often there is fire when we can see smoke

P(Smoke|Fire) means how often we can see smoke when there is fire

So the formula kind of tells us "forwards" P(Fire|Smoke) when we know "backwards" P(Smoke|Fire)

Example:

dangerous fires are rare (1%)

but smoke is fairly common (10%) due to barbecues,

and 90% of dangerous fires make smoke

We can then discover the probability of dangerous Fire when there is Smoke:

P(Fire|Smoke) =  P(Fire) P(Smoke|Fire)P(Smoke)

=  1% x 90%10%

= 9%

So it is still worth checking out any smoke to be sure.