discrete markov stochastic process

hi guys

I have a simple problem driving me crazy :)

the topic is stochastic process and markov process, this is the problem:

Quote:

assuming every day's weather has only two options: rainy or sunny.

the probability that in certain day the weather is the same as the day before is

. the probability of change in weather is

.

now i will define

as a discrete time stochastic process as:

if the n'th day was rainy and

if the n'th day was sunny.

the question is: given that today, n=0, is a rainy day, find the probability to rain in the n'th day. clue: you can organize the data in a matrix.

i've tried few approaches but nothing comes out, i know its simple, will be happy for assistance. thanks :)