The probability of rain on any particular day is 0.2. However, the probability of rain on a day after a rainy day is 0.85, whereas the probability of rain on a day after a non-rainy day is 0.1.

a) On two consecutive days, find the probability of having:

i. two rainy days

ii. exactly one rainy day

iii. at least one dry day

b) On three consecutive days, find the probability of having:

i. three rainy days

ii. exactly one dry day

iii. at most two rainy days