Subjects probability

Probability Toffee 8216Ef

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1. **State the problem:** We want to find the probability that both chocolates picked are toffee, given the tree diagram with probabilities. 2. **Understand the tree diagram:** - Probability of first chocolate being Toffee = $\frac{3}{8}$ - Given first is Toffee, probability second is Toffee = $\frac{2}{7}$ 3. **Formula for combined probability:** The probability of both events happening in sequence is the product of their probabilities: $$P(\text{both Toffee}) = P(\text{first Toffee}) \times P(\text{second Toffee | first Toffee})$$ 4. **Calculate:** $$P(\text{both Toffee}) = \frac{3}{8} \times \frac{2}{7} = \frac{6}{56}$$ 5. **Simplify the fraction:** $$\frac{6}{56} = \frac{3}{28}$$ 6. **Final answer:** The probability that both chocolates are toffee is $\frac{3}{28}$.