Same Same But Different - Part 2

Probability Level 2

When we roll 2 fair 6-sided dice, they are either the same of they are different.

Which is more likely? They are the same, or they are different?

They are different Equally Likely They are the same

1 solution

Zee Ell
Sep 19, 2016

There are 6 possible values (integers between 1 and 6) we can get if we cast a fair (6 sided) die.

We can get these values on both dice in 6 of the 6 × 6 = 36 cases.

$\text { (Probability: } \frac {6}{36} = \frac {1}{6} )$

In all the other (30 out of 36) cases. we get different values on the 2 dice.

$\text { (Probability: } \frac {30}{36} = \frac {5}{6} )$

Hence, our answer should be, that it is more likely, that:

$\boxed { \text {They are different. } }$