1. **State the problem:** We want to find the probability that both chocolates picked are toffee, given the tree diagram probabilities.
2. **Understand the tree diagram:**
- First chocolate can be Mint with probability $\frac{5}{8}$ or Toffee with probability $\frac{3}{8}$.
- If the first is Mint, second chocolate can be Mint with probability $\frac{4}{7}$ or Toffee with probability $\frac{3}{7}$.
- If the first is Toffee, second chocolate can be Mint with probability $\frac{5}{7}$ or Toffee with probability $\frac{2}{7}$.
3. **Identify the event:** Both chocolates are the same flavour and specifically both are Toffee.
4. **Calculate the probability of both being Toffee:**
- Probability first chocolate is Toffee: $\frac{3}{8}$
- Given first is Toffee, probability second is Toffee: $\frac{2}{7}$
5. **Use the multiplication rule for dependent events:**
$$P(\text{Toffee and Toffee}) = P(\text{First Toffee}) \times P(\text{Second Toffee} | \text{First Toffee}) = \frac{3}{8} \times \frac{2}{7}$$
6. **Multiply the fractions:**
$$\frac{3}{8} \times \frac{2}{7} = \frac{6}{56}$$
7. **Simplify the fraction:**
$$\frac{6}{56} = \frac{3}{28}$$
**Final answer:** The probability that both chocolates are toffee is $\frac{3}{28}$.
Toffee Probability F4F564
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