# Thread: If the die is assumed to be fair, what is the most likely number of sides it has.

1. ## If the die is assumed to be fair, what is the most likely number of sides it has.

Suppose the following experiment is conducted : A die with s sides marked 1 through s is tossed n times and the number of times a 1 is tossed is recorded. After many repetitions of the experiment, it is found that the number of 1's tossed has a mean of 33 and a standard deviation of 5.5.

a). If the die is assumed to be fair, what is the most likely number of sides it has ?

Thank you.

2. Originally Posted by sahip
Suppose the following experiment is conducted : A die with s sides marked 1 through s is tossed n times and the number of times a 1 is tossed is recorded. After many repetitions of the experiment, it is found that the number of 1's tossed has a mean of 33 and a standard deviation of 5.5.

a). If the die is assumed to be fair, what is the most likely number of sides it has ?

Thank you.
Perhaps I'm missing some complexity here, but for a 6-sided die, you'd expect each face value to appear close to one sixth of the time, so I would think that you could simply write

$\frac{n}{s} \approx 33$

and use the nearest integer function when solving, without needing to think about standard deviation.