If you have a two table tennis ball outputting machines acting as Bernoulli trials. The first machine gives a player 1000 balls with p=0.7 of being red and 0.3 yellow. The second gives a player 100 balls with an unknown probability of the Bernoulli. What hypothesis tests can be done to check the similarity of distributions between the first and second machine? How would the test be different if the first machine generates 1000 balls at random them the second machine generates 100 of the 1000 balls and you want to know how likely is it the second machine to create a subsample representative of the first machine sample?

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