2020 HCI EM S4 P2

A box contains \(9\) red cards, \(6\) blue cards and \(3\) yellow cards.

Two cards are drawn at random, without replacement, from the box.

1. Draw a tree diagram to show the probabilities of the possible outcomes.
2. Find, as a fraction in its simplest form, the probability that
   1. the two cards are of the same colour,
   2. the two cards are of different colours.
3. All the cards are placed back in the box.
   The cards are then drawn at random, with replacement, from the box.
   1. Find the probability that exactly \(2\) blue cards are being drawn out of \(3\) draws.
   2. Find the probability that at least a yellow card is being drawn out of \(5\) draws.