Differently Numbered Dice

Probability Level 1

I have two fair six-sided dice. One of the dice has the standard numbers on its faces: 1, 2, 3, 4, 5, and 6. The other die has non-standard numbers on its faces: 1, 1, 1, 1, 1, and 16.

I roll each die a large number of times, and it seems that the average roll is the same value (3.5) for both dice. However, if I roll both dice at the same time, which die has a greater chance of rolling higher?

Both dice have the same chance to roll higher The standard die The non-standard die

1 solution

Jordan Cahn
Oct 8, 2018

The non-standard die will be higher only when it rolls 16 (no matter what the standard die shows). This occurs with probability $\frac{1}{6}=\frac{6}{36}$ .

The standard die will be higher when it rolls anything but a 1 and the non-standard die rolls a 1. This occurs with probability $\frac{5}{6}\times\frac{5}{6}=\frac{25}{36}$ .

Thus, the standard die has a greater probability to be higher.

Differently Numbered Dice

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