The applet below simulates sampling from the urn containing N balls. The total number of balls in urn, the number of red balls, and the sample size can be stated by the user. Sampling can be done with or without replacement.
Answer the questions below with Sampler. Pick a population size of N = 10 and sample size of n = 2. If the probability of selecting a red ball is 0.8, the number of red balls in population (randomly positioned) is 10 x 0.8 = 8.
1. Determine the probability of getting two 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?
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?