MHB Do independent experiments add to probability?

[karamand]

There are two categories of objects, A and B.
From long term observation, experiment 1 is known to be 70% accurate i.e. it predicts type A or B correctly in 70% of cases.
Experiment 2 is totally independent. It uses different methods and different characteristics. It is also known to predict correctly in 70% of cases.
If both experiment 1 and experiment 2 predict type A, what is the probability that it is type A. Does the fact that both experiments predict the same outcome add to my certainty?

 

[chisigma]

There are two categories of objects, A and B.
From long term observation, experiment 1 is known to be 70% accurate i.e. it predicts type A or B correctly in 70% of cases.
Experiment 2 is totally independent. It uses different methods and different characteristics. It is also known to predict correctly in 70% of cases.
If both experiment 1 and experiment 2 predict type A, what is the probability that it is type A. Does the fact that both experiments predict the same outcome add to my certainty?

The probability of correct reasult in case of single test is $P = 1 - .3 = .7$... in case of two tests is $P = 1 - (.3)^{2} = .91$... on case of three test is $P= 1 - (.3)^{3}= .973$ and so on...

Kind regards

$\chi$ $\sigma$

 

[karamand]

Thanks - that's what I intuitively felt. The additional test added to my confidence. Do you have any reference to the theory behind this?

Regards
Phil