I don’t understand what you mean by “simulate”.
If you just want to play games with the variation around a .271 or a .300 batting average over time the easiest thing to do is take a thousand samples – in the first case 271 1’s and 729 0’s and in the second case 300 1’s and 700 0’s. Put them in two columns with 271 1’s followed by 729 0’s (or the other way around – it doesn’t matter) and the same for the 300 and 700. Then find a random number generator function out on the web and have it generate a random sequence of integers from 1 to 1000 (sampling without replacement so you only get each integer once). Do this twice and then match the random column one-to-one with the 0’s and 1’s column and then sort the two columns by the random number column so the random numbers are in sequence from 1 to 1000. This will result in a random draw for the 0’s and 1’s and you can take any sub-sample of any size (1-50, 35-220, 14-700, etc.) and compute the batting averages for those sub-samples and see what you see.
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