At Least One Six

Think about the complementary event of never rolling a 6.

Each roll independently avoids a 6 with probability $5/6$.

1. 1. Complement

   It is easier to compute the probability of no 6 in four rolls.

2. 2. Independence

   Each roll avoids 6 with probability $5/6$, and rolls are independent.

   $$P(\text{no 6})={\left(\frac{5}{6}\right)}^4$$

3. 3. Complement rule

   Subtract from 1 to get at least one 6.

   $$P=1-{\left(\frac{5}{6}\right)}^4\approx 0.5177$$

Answer: 1 - (5/6)^4