Mr.Smith lives in Glasgow, Scotland, where it rains 25% of the time, it is sunny 25% of the time, and it is cloudy 50% of the time. Every morning Mr.Smith looks out of the window before leaving the house, to decide whether to take an umbrella or not. If it rains, he takes an umberlla with a probability of 90%(i.e. he forgets to take it with a probability of 10%). If its is cloudy, he takes an an umbrella with a porbabilty of 20%(because Mr.Smith is a pessimist).

i). What is the probability that Mr.Smith leaves the umbrella at home?

ii). If Mr.Smith leaves the house with the umbrella, what is the probability that it will be sunny?