Question: Quant developer interview question:

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> There are two price prediction models, one with accuracy 55%, another with accuracy 65%, both predict price is gonna go up, what's the probability that price is gonna go up? Please provide detailed answer.
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One can assume two predictions are independent.

Answer: 
A simple answer here.

We construct random variable X representing correctness of model 1. X=1 if model 1 is correct, 0 otherwise. Similarly we define Y for model 2.

Consider Pr(model 1 is correct and model 2 is correct|both are correct or both are wrong), since we know they give same prediction, thus we have this condition of both correct or both wrong.

It's easy to calculate the probability: $\frac{0.55\*0.65}{0.55\*0.65+0.45\*0.35}=0.6942$.

Thus with 0.6942 probability, the price grows up.
This could be considered an example of aggregate data meta-analysis. 

Before pooling the two estimates, you need to provide also the variability in such effect estimates with a standard error or equivalent.

Then you can simply perform pooling with fixed effect inverse variance weighting.