This STEM project is to use JAVA random simulation to differentiate statistics between Binomial (with replacement) and Hypergeometric (without replacement). The author used the Powerball lottery probability to determine the Jackpot probability by matching the numbers of five balls and the Mega number.  The Mega number of the red ball can be duplicated the same number of any white ball picked already.  There is about 12% higher probability for Jackpot if the Mega number cannot duplicate the ball of any white ball picked. The author derived the JAVA script to simulate two probability scenarios. Binomial Approximation of Hypergeometric Probability by adjusting the sample size in the pool was also studied.  When the pool size is larger, the probability difference between whether the Mega number can duplicate the white ball number becomes smaller.  The ratio of two probabilities will approach 1 when the pool size becomes larger.  JAVA script can demonstrate this Probability Approximation pattern.  This STEM project is successful since the author can integrate learning across Statistics, and JAVA as a Data Science approach.