Question

You rolled the dice 10 times and got 6-point for 5 times. Suppose you no longer believe the dice is fair. What is the estimated probability of getting 6-point each time you roll the dice?

Answer 1

The estimated probability of rolling a 6-point with this particular die, based on the 10 rolls provided, is 0.5 or 50%. This is much higher than the probability of 1/6 (about 16.7%) expected for a fair six-sided die.

Step-by-step explanation:

If you rolled a die 10 times and observed a 6-point result 5 times, one might suspect the die is biased based on this small sample. To estimate the probability of rolling a 6-point with this potentially biased die, you can use the relative frequency approach. The estimated probability would be the number of times a 6 appeared divided by the total number of rolls. Since you observed a 6-point 5 times out of 10 rolls, the estimated probability (P(6)) would be 5/10 or 0.5 (50%).

This estimate suggests that in this particular set of rolls, a 6-point was rolled with a probability of 0.5, which is significantly higher than the expected probability of 1/6 (approximately 0.167) for a fair six-sided die. To determine if the die is truly biased or if this was due to chance, a larger number of trials would need to be conducted.