Suppose there are 1 million parts from which 1% are defective i.e 10000 part are defective. Now I am taking different sample sizes from 1 million which are 10%,30%,50%, 70% and 90% of original population i.e 1 million. I want to find probability of detecting 5000 defective parts from each sample independently. issue is suppose I am finding probability of maximum 5000 defective parts in any sample size below 50% of population, the answer is 0, Here p value is 0.01 and q is 0.99. At 50% of total population, probability of finding 5000 defective parts is 0.5 and sample sizes above 50% gives probability 1. In all sample size value of p is 0.01 and number of defective parts is 5000. Only sample size is changing. Now here we have so difference from 0 to 0.5 and then 1. there are no intermediate values between them although we are changing sample size linearly. Can someone plz tell me the problem. I really need to solve it