A tube contains 20,000,000 particles in total. Of these particles, 40,000 are blue and 19,960,000 are red. So, for every 500 blue particles, there is 1 red particle. If I were to remove 50,000 particles at random, what is the probability that I will obtain 80 red particles and 39,920 blue particles (the 'true' ratio of the population in the sample tube)?

How many times would I need to repeat this measurement, so that the averaged ratios (red:blue particles) represented the true ratio, with a p < 0.05?

If possible, please show me how your calculated this, so I can repeat with different values (for instance, if I were to take 100,000 particles per each sampling).

Thanks much!!