The applet below simulates sampling from an urn containing N balls. The total number of balls in the urn, the number of red balls, and the sample size can be determined by the user. Sampling can be done with or without replacement.
Answer the questions below with the Sampler. Select a population size of N = 10 and a sample size of n = 2. If the probability of choosing a red ball is 0.8, the number of red balls in the population (randomly positioned) is 10 x 0.8 = 8.
1. What is the probability of getting two (2) red balls if sampling is done without replacement? Compute this exactly.
2. Estimate this probability by doing 25 runs. How good is your estimate?
3. Do another 25 runs and record the combined estimate of the probability. Did your estimate improve? Discuss.
4. What is the probability of getting two red balls if sampling is done with replacement? Compute this exactly.
5. Estimate this probability by doing 25 runs. How good is your estimate?
6. Do another 25 runs and record the combined estimate of the probability. Did your estimate improve? Discuss.
7. Why is the probability of getting two red balls when sampling without replacement close to the probability of getting two red balls when sampling with replacement?