Suppose you roll a die and earn whatever face you get. What is the expected return? Now suppose you have a chance to roll a second die. If you roll, you forfeit your earnings from the first round. When should you roll the second time?

Hard Difficulty

Hard questions require advanced understanding and critical thinking. Here, your problem-solving skills are key, as these questions often involve complex scenarios needing in-depth analysis and well-structured responses.

Statistics question

Statistics questions assess your understanding of data analysis principles. Show your knowledge of probability, statistical inference, experimental design, and how you apply quantitative methods to interpret data and draw valid conclusions.

Here's a Hint

Calculate the expected value of a single die roll, then determine when the first roll has a value below this expectation, making a second roll advantageous.