1. **State the problem:** Martin has 5 plain and 3 stripy socks, total 8 socks. He picks one sock at random, then picks a second sock at random without replacement. We want to find the probability that both socks chosen are stripy. 2. **Understand the tree diagram:** The first choice splits into two branches: Plain with probability $\frac{5}{8}$ and Stripy with probability $\frac{3}{8}$. 3. **Calculate second sock probabilities:** - If the first sock was Plain, then 7 socks remain: 4 Plain and 3 Stripy. - Probability second sock is Plain: $\frac{4}{7}$ - Probability second sock is Stripy: $\frac{3}{7}$ - If the first sock was Stripy, then 7 socks remain: 5 Plain and 2 Stripy. - Probability second sock is Plain: $\frac{5}{7}$ - Probability second sock is Stripy: $\frac{2}{7}$ 4. **Complete the tree diagram probabilities:** - Plain then Plain: $\frac{5}{8} \times \frac{4}{7} = \frac{20}{56}$ - Plain then Stripy: $\frac{5}{8} \times \frac{3}{7} = \frac{15}{56}$ - Stripy then Plain: $\frac{3}{8} \times \frac{5}{7} = \frac{15}{56}$ - Stripy then Stripy: $\frac{3}{8} \times \frac{2}{7} = \frac{6}{56}$ 5. **Find the probability of two stripy socks:** This is the branch Stripy then Stripy. $$P(\text{two stripy}) = \frac{3}{8} \times \frac{2}{7} = \frac{6}{56} = \frac{3}{28}$$ 6. **Final answer:** The probability Martin chooses two stripy socks is $\boxed{\frac{3}{28}}$.