Suppose an urn contains 100 marbles, 75 red and 25 black. A marble is drawn at r
ID: 3021103 • Letter: S
Question
Suppose an urn contains 100 marbles, 75 red and 25 black. A marble is drawn at random from the urn and you are asked to guess what colour you believe the marble to be. The marble is then shown, replaced, and the urn's contents again randomised. The aim is to maximise the number of correct guesses. Before reading any further, what strategy would you employ? What would you guess? Assume 4 red marbles come out in a row. What would your next guess be? Why? Include a brief discussion of the gambler's fallacy.Explanation / Answer
Answer:
Well, if the marbles are being replaced, you are going to have a 75/100 or 3/4 probability of making the correct choice if you say red. In this case, despite the fact that 4 reds have already come up, it is still most likely (most probable) that a red will come up the next time. Draws before have to determination of the outcome of the next draw since we are replacing the marble each time. As long as it remains a 3 out of 4 probability with each successive draw of getting a red marble over a black marble, red is the color you will repeatedly pick in this situation regardless of whether the marble drawn before was red or black.