2023 HCI J2 MYE P2 Q10

John has a collection of \(230\) Rego bricks. Rego bricks come in \(3\) different sizes and \(4\) different colours. Bricks of the same size and colour are identical. The number of Rego bricks of each size and colour are shown in the table below

John puts all the Rego bricks in a bag and picks one brick at random.

1. 1. Find the probability that this brick is large and red.[1]
   2. Find the probability that this brick is either small or white.[2]
   3. Find the probability that this brick is either medium or large, given that it is not blue.[3]

John now puts all the Rego bricks back in the bag and chooses two bricks at random without replacement.

2. Find the probability that the two chosen bricks include exactly one small brick and exactly one red brick.[3]
3. Among the \(12\) possible size and colour combinations, it is given that the probability of John choosing two bricks of \(2\) particular size and colour combinations that are different is \(\frac{11}{1145}\). Write down the size and colour combinations of these two bricks.[3]