probability and set

[amit bhardwaj]

Que.1 what is prior and posterior probability?

Que.2 Let A,B,C,D be arbitary set then

     

        show that (A intersection B)*(C intersection D)=(A intersection C)*(B intersection D) ?

Que.3 Let A,B,C be arbitary set then

     

        show that   (A-B)-C=(A-C)-(B-C) ?

[Kapil Gupta]

On Thursday, September 10, 2015 at 12:43:45 PM UTC+5:30, amit bhardwaj wrote:

Que.1 what is prior and posterior probability?

Prior Probability is probability given or stated by an observer/experience.
Posterior Probability is the probability of that a specific cause has actually resulted into the effect.
For example:

Consider that 3 machines M1, M2, M3 each produces toys in a factory.
M1 produces 20%
M2 produces 30%
M3 produces 50%
This produce percentage is known from the productivity of machines.

Also, some of the toys are defective, the probability that M1, M2 and M3 produce defective toys is 0.02, 0.5 and 0.3 respectively.
Such probabilities that cannot be found directly, but an expert or experienced person can tell is called Prior probabilities

Now, there could be another type of probability that

a toy we picked at random and is found to be defective, what is the probability that M1 has produced it.

Such probabilities which are looking back at the reason of an effect is called posterior probability

Que.2 Let A,B,C,D be arbitary set then

     

 

        show that (A intersection B)*(C intersection D)=(A intersection C)*(B intersection D) ?

What is * operation?

Que.3 Let A,B,C be arbitary set then

     

        show that   (A-B)-C=(A-C)-(B-C) ?

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