The weather in Bitsburg on any given day can be classified as sunny, cloudy or partially cloudy. Each day is also classified as dry or wet (i.e. rain, snow, sleet, etc.). The probability of a sunny day in Bitsburg is 0.48, and the probability of a cloudy day is 0.37. Additionally, it is known that the probability of a sunny and dry day 0.45. The probability of a cloudy and dry day is 0.14. The probability of a partially cloudy and dry day is 0.06.
a) Find the probablity of a dry day.
b) Find the probability of a wet day.
c) Find the probability of a sunny day, given that it is a dry day.
d) Find the probability of a dry day, given that it is a sunny day
e) Find the probability of a cloudy day, given that it is a wet day.
f) Is a dry day independent of a sunny day? Answer mathematically.