A box contains 2 green apples and 2 red apples. Apples are taken from the box, one at a time, without replacement. When both red apples have been taken, the process stops. The random variable X is the number of apples which have been taken when the process stops.

i. Show that P(X = 3) = 1/3.

ii. Draw up the probability distribution table for X.

Another box contains 2 yellow peppers and 5 orange peppers. Three peppers are taken from the box without replacement.

iii. Given that at least 2 of the peppers taken from the box are orange, find the probability that all 3 peppers are orange.