in a certain board game, a 12 - sided number cube showing numbers 1 - 12 is rolled. if three such number…

Explanation:

Step1: Find probability of not getting 2

The probability of not getting a 2 on a single 12 - sided die roll is $\frac{11}{12}$ since there are 11 non - 2 outcomes out of 12 possible outcomes.

Step2: Find probability of not getting 2 on three rolls

Since the rolls are independent events, the probability of not getting a 2 on all three rolls is $(\frac{11}{12})^3=\frac{11^3}{12^3}=\frac{1331}{1728}\approx0.7703$.

Step3: Find probability of getting at least 1 2

The probability of getting at least 1 2 is the complement of the probability of getting no 2s. So it is $1 - (\frac{11}{12})^3=1-\frac{1331}{1728}=\frac{1728 - 1331}{1728}=\frac{397}{1728}\approx0.2297$.

Answer:

0.2297