The coat of a certain breed of cat can be either black, white or grey.

When a black-coated male is crossed with a white-coated female, the offspring kitten has a 50% chance of having a black coat, and a 50% chance of having a white coat.

When a white-coated male is crossed with a white-coated female, the offspring kitten has a 20% chance of having a black coat, a 60% chance of having a white coat and a 20% chance of haing a grey coat.

When a grey-coated male is crossed with a white-coated female, the offspring kitten has a 10% chance of having a black coat, a 45% chance of having a white coat and a 45% chance of having a grey coat.

(a) Assume that each successive generation of cats is produced by crossing all cats with a white-coated female. Write down the transition matrix for this Markov process.

(b) If initially there are equal numbers of black-coated and white-coated cats, and no grey-coated cats, what percentage of the next generation will be grey-coated?

(c) In the long run, what percentage of cats will have black, white and grey coats?