7 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.
- Show that \(\mathrm { P } ( X = 3 ) = \frac { 1 } { 3 }\).
- Draw up the probability distribution table for \(X\).
Another box contains 2 yellow peppers and 5 orange peppers. Three peppers are taken at random from the box without replacement.
- Given that at least 2 of the peppers taken from the box are orange, find the probability that all 3 peppers are orange.