You visit your grandparents and notice an old die and notebook. The die is handmade and the edges are worn. Grandpa explains that he rolled this die 10,000 times, independently and under the same conditions, when he was a prisoner of war and recorded the results of the die rolls in his notebook:
- Side of the die 1 2 3 4 5 6
- Number of outcomes 2607 1633 1148 1839 2552 221
He adds that he used to run an illegal gambling ring and that he fashioned this die out of bone himself. Which of the following follow from these observations? I. The data suggests the die has a much lower probability of producing a ‘6’ compared to other outcomes. II. It is possible, though very unlikely, that the die is fair.
How do I determine if the die is fair? The P(6) here is 0.0221 and if I'm not wrong, both options I and II are correct?