Subjects probability

Toffee Probability F4F564

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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 $\frac{3}{28}$.