We propose a new approach, Bayesian Probability of Association (BPA) which takes into account the probability distributions of information and noise in the variables and uses Bayesian statistics to predict associations better than existing approaches. Our approach overcomes the limitations of linearity of the relationship and normality of the data, assumed by the Pearson correlation coefficient. It is different from the current measures of association because considering information separately from noise helps identify the association in information more accurately, makes the approach less sensitive to noise and also helps identify causal directions. We tested the approach on 15 datasets with no underlying association and on 75 datasets with known causal relationships and compared the results with other measures of association. No false associations were detected and true associations were predicted in more than 90% cases whereas the Pearson correlation coefficient and mutual information content predicted associations for less than half of the datasets.