I'm a physician and really need help from somebody who is good at probability. I calculated time series of tidal stresses. It turned out that the probability of having positive tidal stress is 0.45 and negative - 0.55 (I counted up number of hours when the stress was positive/negative and divided by the total number of hours). Usually you would expect to have 0.5 for positive stress and 0.5 for negative. So now, if we assume that an earthquake occurs at random, does it mean that there is 0.45 chance that it happens when the stress is positive? if yes, what is the probability that this earthquake occurs within some one particular hour when the stress is positive (e.g. within one hour centred on a max tidal stress)? Is it also 0.45?

I'd be really grateful if somebody can help me with it. Thanks a lot

You should be right. A factor that may cause your conclusion to be incorrect is if there would be some peculiar relationship between tidal stress and earthquake occurance, e.g. if an earthquake has a greater chance of occuring when tidal stress is negative. But that is probably not the case.