Suppose I roll a die 142 times and get the following distribution {1: 0.134, 2: 0.197, 3: 0.169, 4: 0.183, 5: 0.162, 6: 0.155}, how do I estimate if it is a fair die (i.e., what's the probability that the die is fair)?
I don't need an exact solution but what mathematical tools can I use to solve this problem?
Edit: you can assume the rolls are iid.
There is no way of calculating the probability of a fair die given the distribution of rolls. However, a hypothesis test can be performed to accept/reject that the die is fair, which is a classical example of Pearson's chi-squared test.
Credits to Adam. See details in the comment section.