I know the statement that the previous event won't affect the current event.
But what if the statistic of the previous results(large amount of data) shows that the probability of one particular ball appears is higher than other balls (for example if there are five balls numbered as 1,2,3,4,5. The statistic shows that ball number 5 has a higher probability than 1/5, since the balls are not perfect sphere). Then I can state that I have a higher winning chance if I choose ball number 5.
It seems the previous result do affect my choices. Is there contradiction between those two statements？