1. **State the problem:** We have a biased dice where the probability of rolling a 6 is $\frac{1}{5}$. We want to complete the tree diagram for two rolls and find the probability of rolling two sixes in a row. 2. **Identify probabilities:** The probability of rolling a 6 is $P(6) = \frac{1}{5}$. The probability of not rolling a 6 is the complement: $$P(\text{not }6) = 1 - P(6) = 1 - \frac{1}{5} = \frac{4}{5}$$ 3. **Complete the tree diagram:** - For the first roll, branches are: - Roll 6: $\frac{1}{5}$ - Roll not 6: $\frac{4}{5}$ - For the second roll, the probabilities are the same regardless of the first roll outcome (assuming independence): - Roll 6: $\frac{1}{5}$ - Roll not 6: $\frac{4}{5}$ 4. **Calculate the probability of rolling two sixes:** - This is the probability of rolling a 6 on the first roll AND a 6 on the second roll. - Since rolls are independent, multiply the probabilities: $$P(6 \text{ then } 6) = P(6) \times P(6) = \frac{1}{5} \times \frac{1}{5} = \frac{1}{25}$$ 5. **Final answer:** The probability of rolling two sixes in a row is $\boxed{\frac{1}{25}}$.