An amateur meteorologist has a rain gauge outside of her house which she empties daily. Suppose that she records whether or not there was any rain each day for a week. Her data consist of a string of 7 values with R representing rain and N representing no rain.

a) (3 points) List three possible outcomes in the sample space.

b) (3 points) Identify two compound events that are mutually exclusive. Describe the events in words and by listing the outcomes they contain.

c) (3 points) Identify two compound events that are not mutually exclusive. Describe the events in words and by listing the outcomes they contain.

d) (2 points) Provide an interpretation for the following statement: The probability that it rains on two out of the seven days is .25.

e) (4 points) Suppose that we considered all outcomes to be equally likely. What would this imply about the probability that it rains on any given day?