flavoured with either caramel or raspberry. The possible outcomes of Alex picking two chocolates at random are shown in the tree diagram below.
If both chocolates are the same flavour, what is the probability that they are both raspberry? Give your answer as a fraction in its simplest form.
First chocolate
Second chocolate
Answer
Calculate the conditional probability: P(R1 and R2 | S) = P(R1 and R2) / P(S) = 0.25 / 0.5 = \(\boxed{0.5}\)
Step 1 ：Calculate the probability of picking two raspberry chocolates: P(R1 and R2) = P(R1) * P(R2|R1) = 0.5 * 0.5 = \(0.25\)
Step 2 ：Calculate the probability of both chocolates being the same flavor: P(S) = P(R1 and R2) + P(C1 and C2) = 0.25 + 0.25 = \(0.5\)
Step 3 ：Calculate the conditional probability: P(R1 and R2 | S) = P(R1 and R2) / P(S) = 0.25 / 0.5 = \(\boxed{0.5}\)
