Question

The following sampling proposal is flawed. Explain why and what you could do to fix the issue.

A mathematician wants to test the probability he calculated for drawing colored balls randomly from a bag. He buys a bag of colored marbles from a local store, puts them in a bag, draws them repeatedly and records the results. Assuming his calculations are correct, suggest some reasons why the results of drawing from the bag might not match the calculated results.

Answer 1

A mathematician buys a bag of coloured marbles from a local store, puts them in a bag, draws them repeatedly and records the results to test the probability he calculated for drawing coloured balls randomly from a bag.

The sampling proposal is flawed and the results of drawing from the bag might not match the calculated results. This is because he is simply drawing ball repeatedly however he is not replacing them changing the probability of drawing balls each time he draws one ball

To fix the issue he can draw the balls with replacement. i.e if he draws a ball he has to place it back before next draw so that the probability to draw ball remain same hereafter