Hanna has 12 hollow chocolate eggs, and each one contains a sweet. The eggs are identical in appearance, but Hanna knows that 3 hold a red sweet, 4 hold an orange sweet and 5 hold a yellow sweet. One after another, Hanna’s three children each selects one egg at random and eats it, keeping the sweet inside.
(a)[4]
Find the probability that the 3 chosen eggs all contain a sweet of the same colour.
(b)[2]
Find the probability that all 3 chosen eggs contain a yellow sweet, given that all three children have sweets of the same colour.
(c)[3]
Find the probability that at least one of Hanna’s three children chooses an egg containing an orange sweet.
Worked solution & mark scheme
This 9-mark question has a full step-by-step worked solution and mark scheme. One marking point: “Accurate evaluation of probabilities for cases such as YYY, OOO, RRR” …