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How does my broker (optionsXpress) calculate probabilities that the stock will hit a certain price?
Their algorithm may be different (and proprietary), but how I would to it is to assume that daily changes in the stock are distributed normally (meaning the probability distribution is a "bell curve" - the green area in your chart).  I would then calculate the average and standard deviation (volatility) of historical returns to determine the center and width of the bell curve (calibrating it to expected returns and implied volaility based on option prices), then use standard formulas for lognormal distributions to calculate the probability of the price exceeding the strike price. So there are many assumptions involved, and in the end it's just a probability, so there's no way to know if it's right or wrong - either the stock will cross the strike or it won't.