A jar contains 3 lemon sweets and 5 orange sweets. A sweet is drawn at random, its flavour is noted and it is PUT BACK; then a second sweet is drawn. What is the probability that the two sweets drawn have the same flavour?

Because the first sweet goes back, both draws face the same 8 sweets. P(both lemon) = (3/8)(3/8) = 9/64 and P(both orange) = (5/8)(5/8) = 25/64, so the answer is 34/64 = 17/32. The option 15/32 = 30/64 is the probability of two DIFFERENT flavours, and the two must add to 1, which they do. Answering 15/64 counts only the lemon-then-orange order and forgets the reverse, and 1/2 would need the two flavours to be equally common.