Question

Alex has a box of chocolates which are all 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.

Answer 1

The probability that both chocolates are the same flavor is 64/17 in its simplest form.

To find the probability that both chocolates are the same flavor, we need to consider the cases where both chocolates are either caramel or raspberry. From the given tree diagram, we can see that there are two cases where both chocolates have the same flavor:

Both chocolates are raspberry: There is only one possible outcome for this case, represented by the node (47, 11).

Both chocolates are caramel: There are two possible outcomes for this case, represented by the nodes (12, 12) and (5, 11).

Now, we can calculate the probability for each case:

Raspberry: 47/17

Caramel: 17/17

To find the total probability, we can add the probabilities of both cases:

Total probability = 47/17 + 17/17

Total probability = 64/17.

Therefore, the probability that both chocolates are the same flavor is 64/17 in its simplest form.