[ASK] Is Expected Frequency Rounded Up or Down?

Apr 2018
A die is tossed 100 times. What's the expected frequency that the number appears will be 4?

The probability is 1/6, so the expected frequency is 1/6 × 100, but that results in a fraction (16 2/3). Do we need to round it up or down? Is the answer 16 or 17?


MHF Helper
Nov 2013
You don't need to round it at all. The correct answer is $\dfrac{50}{3}$

True you won't see 2/3 of a die but that doesn't matter. An expectation is an average and as such there's no reason to expect it must be an integer.
Aug 2007
If you are forced to round, for whatever reason, you will need to decide exactly how to do that.

Typically, a simple up or down methodology will prove unsatisfactory as you will violate the definition of a probability distribution:

Down 2 dp
1/3 = 0.33
1/3 = 0.33
1/3 = 0.33
0.33 * 3 = 0.99 and that is NOT 1.00

Likewise, fudging (forced footing) proves unsatisfactory:

1/3 = 0.33
1/3 = 0.33
1/3 = 0.34

They are not really equal, are they.

Unless you are in a purely theoretical pursuit, you just have to make up your mind what is and is not suitable.