# Do independent experiments lend extra weight to probability?

#### Nquisitive

##### New Member
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?

#### hlsmith

##### Omega Contributor
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?
Is this just a question or do you have data? So experiment 1 predicts A correctly 70% of the time and independently experiment 2 correctly predicts A 70% of the time using a different mechanism. If you had data you could fuse the two groupings of predictors together.

What is the temporality of the tests. I am not a Bayesian, but they would say if one test was performed then the next, you could use the results as the prior (pre-experiment) probability for the next. Do you know the prevalence of the outcome from the population sampled?

#### rogojel

##### TS Contributor
Hi,
a kind of Bayes like analysis would lool like this: Assuming that As and Bs are equally likely ( is this the case?) imagine you have 100 true As and 100 true Bs,

From the 100 true As you will get 49 that are identified as A by both methods. You will also get 9 that are in fact Bs but were erroneously identified as As by both methods. ( and 42 mixed ratings BTW) So the probability that an object is A if it got a double A rating is

49/(49+9)=49/58=84.5%

You can easily extend the analysis for the case where As and Bs are not equally probable or where the method's accuracies are differrent.

regards