There are only purple beads and green beads in a bag. The number of purple beads is three times the number of green beads. Beth takes at random one bead from the bag. She records the colour of the bead and then replaces it in the bag. Beth does this n times, where n ≥ 2 Write down an expression, in terms of n, for the probability that Beth gets a purple bead at least once and a green bead at least once.
