Question

I want to test to see if a die is fair. Why shouldn’t I just do one test to see if there are too many ones, one test to see if there are too many twos, one test to see if there are too many threes, etc.?

Answer 1

Solution:

First we need to understand the meaning of fair die.

Fair die means each of the faces having equal or same probability of landing on that face. Each having equal chance to occur. Therefore, the probability of each face is 1/6.

Now, need to understand about the loaded die. The loaded die is designed in a special way that 3 or 4 are relatively likely to occur and other faces are unlikely to occur. Therefore, it does not have equal chance which leading unequal probability of each face. Hence, we should not test to see if there are too many one's, one test to see if there are too many two's, one test to see if there are too many three's and so on.

Done